Fig above shows a wave traveling through a medium. Use the fig to answer the questions below.

A.)What is the amplitude of the wave ? Include correct units.
B.)Use the graph to determine the time of one wave. Use it to find the frequency.
C.)If the speed of the wave is 25 m/s, what is the wavelength of the wave ? Show data listing, equation , substitution leading to the answer for full credit.

The correct answer is Option B. The statement "they have the same A-number but different Z-number" is true .

Atoms of the same element only differ because one of the atoms has more electrons, making it an ion.

This difference does not affect the mass of the atom, which is determined by the sum of its protons and neutrons, represented by the atomic mass or A-number.

The number of protons in an atom is called the atomic number or Z-number.

The Z-number of an element is unique to it. All the atoms of a given element have the same number of protons.

Thus, for example, all carbon atoms have six protons, making the Z-number of carbon 6.

However, different isotopes of an element can have different numbers of neutrons.

This means that they have a different atomic mass or A-number.

Therefore, they have the same A-number but different Z-number.

Therefore the correct Option is B.

For more questions on Atoms

https://brainly.com/question/6258301

#SPJ8

The total volume of the piece of wood is 1.33[tex]cm^3[/tex].

To calculate the total volume of the piece of wood, we can use the principle of displacement.

1. First, we need to find the difference in volume between the two water levels. The initial volume is 17.7 [tex]cm^3[/tex], and the final volume is 18.5 cm^3. The difference is 18.5 [tex]cm^3[/tex] - 17.7 [tex]cm^3[/tex] = 0.8 [tex]cm^3[/tex].

2. Now, we need to find the volume of water displaced by the piece of wood. Since the relative density of the wood is 0.60, it means that the wood is 0.60 times denser than water.

3. The volume of water displaced by the wood is equal to the difference in volume divided by the relative density of the wood. So, the volume of water displaced is 0.8 cm^3 / 0.60 = 1.33 [tex]cm^3[/tex].

4. Finally, the total volume of the piece of wood is equal to the volume of water displaced. Therefore, the total volume of the piece of wood is 1.33 [tex]cm^3[/tex].

For more question displacement

https://brainly.com/question/321442

#SPJ8

(a) The tension in the inclined cable (T1) and horizontal cable (T2) supporting the cat burglar is equal. The tension in the vertical cable (T3) is 524 N.

(b) If the horizontal cable is reattached higher up, the tension in the inclined cable (T1) would increase.

(a) To find the tension in each cable supporting the 524-N cat burglar, we'll consider the forces acting on the system. Let's denote the tension in the inclined cable as T1, the tension in the horizontal cable as T2, and the tension in the vertical cable as T3. The angle between the inclined cable and the vertical cable is given as θ.

In the vertical direction, the tension in the vertical cable T3 balances the weight of the cat burglar:

T3 - 524 N = 0

T3 = 524 N

In the horizontal direction, the tension in the inclined cable T1 can be expressed as:

T1 * cos(θ) = T2

Now, we need to determine the value of θ to calculate T1 and T2. Let's assume that θ is the given angle of θ = 0.

Substituting the angle and rearranging the equation, we have:

T1 = T2 / cos(θ)

T1 = T2 / cos(0)

T1 = T2 / 1

T1 = T2

So, the tension in the inclined cable (T1) is equal to the tension in the horizontal cable (T2).

Therefore, the tension in each cable is as follows:

T1 (inclined cable) = T2 (horizontal cable)

T1 = T2

T3 (vertical cable) = 524 N

(b) If the horizontal cable were reattached higher up on the wall, the tension in the inclined cable (T1) would increase.

The correct answer is option A.  

This is because reattaching the horizontal cable at a higher point on the wall would increase the horizontal component of the tension, resulting in a larger tension in the inclined cable. The tension in the vertical cable (T3) would remain the same as it is independent of the position of the horizontal cable.

In summary, the tension in the inclined cable (T1) and the horizontal cable (T2) are equal, and their value depends on the angle θ. The tension in the vertical cable (T3) is 524 N. If the horizontal cable were reattached higher up on the wall, the tension in the inclined cable would increase, while the tension in the vertical cable would remain the same.

For more such information on: tension

https://brainly.com/question/24994188

#SPJ8

The cardinality of R₁ \ (R₁ intersection A) is 4. The given polynomial (2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35) cannot be solved for x, y, and z due to insufficient equations.

For more questions on cardinality

https://brainly.com/question/32798686

#SPJ8

Guiseppe's buys supplies to make pizzas at a cost of $4.02. Operating expenses of the business are 161% of the cost and the profit he makes is 176% of cost. The regular selling price of each pizza is $7.33.

Let's denote the cost of supplies as C.

Operating expenses:

The operating expenses of the business are 161% of the cost. Therefore, the operating expenses can be calculated as:

Operating Expenses = 1.61 * C

Profit:

The profit made by Guiseppe is 176% of the cost. Therefore, the profit can be calculated as:

Profit = 1.76 * C

Total cost:

The total cost includes the cost of supplies and the operating expenses:

Total Cost = C + Operating Expenses = C + 1.61 * C = 2.61 * C

Regular selling price:

The regular selling price is the sum of the total cost and the profit:

Regular Selling Price = Total Cost + Profit = 2.61 * C + 1.76 * C = 4.37 * C

Given that the cost of supplies is $4.02, we can substitute this value into the equation:

Regular Selling Price = 4.37 * 4.02 = $17.5674

Rounding the final answer to the nearest cent, the regular selling price of each pizza is approximately $7.33.

For more such questions on selling price, click on:

https://brainly.com/question/28420607

#SPJ8

The graphic organizer suggests that the job of an astronaut is complex, demanding, and involves flight.

This conclusion can be drawn by examining the nature of the requirements listed in the graphic organizer. Firstly, the requirements listed in the organizer are numerous and encompass various aspects. They include educational qualifications, such as having a bachelor's degree in a relevant field, as well as specific experience, like piloting an aircraft.

These requirements highlight the complexity of the job and indicate that astronauts need to possess a diverse set of skills and knowledge. Additionally, the requirements for physical fitness and health demonstrate the demanding nature of the job.

Astronauts are expected to undergo rigorous physical training to ensure they can handle the physical stresses associated with space travel and the conditions they will encounter in space. This indicates that the job can be physically exhausting and requires individuals to be in excellent health.

Lastly, the inclusion of flight-related requirements, such as the need to pass a long-duration spaceflight physical and participate in aircraft flights, implies that the job of an astronaut involves actual flight experiences. This indicates that astronauts are directly involved in piloting spacecraft and are expected to have practical experience in flying.

know more about astronaut here:

https://brainly.com/question/30733605

#SPJ8

It takes about 4.85 seconds for the car to accelerate from a speed of 25 mi/h to a speed of 32 mi/h.

The given information includes the acceleration rate of a certain car which is 0.65 m/s², and the initial speed of the car which is 25 miles per hour. The question is asking about the time taken by the car to accelerate from the initial speed of 25 miles per hour to a speed of 32 miles per hour. This is a simple problem in kinematics that can be solved by using the formula of acceleration. Here’s how:
First, convert the initial and final speeds of the car into meters per second.
Given that:
Initial speed of the car, u = 25 miles/hour
Final speed of the car, v = 32 miles/hour
To convert miles/hour to meters/second, multiply it by 0.447:
u = 25 miles/hour × 0.447 = 11.175 meters/second
v = 32 miles/hour × 0.447 = 14.324 meters/second
Now, let’s use the formula of acceleration:
v = u + at
Where,
v = final speed = 14.324 m/s
u = initial speed = 11.175 m/s
a = acceleration = 0.65 m/s²
t = time taken
Substitute the given values in the formula:
14.324 = 11.175 + (0.65)t
Solve for t:
t = (14.324 - 11.175) / 0.65
t = 4.85 seconds
for such more questions on  speed

https://brainly.com/question/13943409

#SPJ8

The force that acts on a projectile in the horizontal direction is Gravitational force.

A projectile is an object upon which the only force is gravity. Gravity acts to influence the vertical motion of the projectile, thus causing a vertical acceleration. The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity.

Due to the absence of horizontal forces, a projectile remains in motion with a constant horizontal velocity. Horizontal forces are not required to keep a projectile moving horizontally. Hence, The only force acting upon a projectile is gravity.

To know more about gravitational force, refer:

https://brainly.com/question/29190673?referrer=searchResults

The magnitudes of the tensions are T1 = mg sin(θ) and T2 = 2mg cos(θ).

In order to find the tensions T1 and T2 in the given system, let's analyze the forces acting on the two blocks. We assume that the incline makes an angle θ with the horizontal.

For the block of mass m, the forces acting on it are its weight mg acting vertically downwards and the tension T1 acting along the incline. The weight can be split into two components: mg sin(θ) perpendicular to the incline and mg cos(θ) parallel to the incline. Since the block is in equilibrium, the sum of the forces along the incline must be zero. Therefore, T1 = mg sin(θ).

For the block of mass 2m, the forces acting on it are its weight 2mg vertically downwards, the tension T2 acting vertically upwards, and the tension T1 acting along the incline. The sum of the forces along the incline for this block is also zero. Therefore, T1 = 2mg sin(θ) and T2 = 2mg cos(θ).

for more such questions on tensions

https://brainly.com/question/24994188

#SPJ8

The function of the power supply is to provide electrical energy to the device or system that needs it. The power supply converts the incoming voltage from the power source into a form that is usable by the device, such as DC voltage.

The readout is a device or component that displays data or information to the user. The readout could be a simple LED display or a complex graphical display.

A peripheral is a device or component that connects to a computer or other electronic device to provide additional functionality. Examples of peripherals include printers, scanners, and external hard drives.

A microcomputer is a type of computer that is designed to fit on a single microchip. Microcomputers are found in a wide range of devices, including smart phones, tablets, and embedded systems.

A transducer is a device that converts one form of energy to another. In electronics, transducers are commonly used to convert electrical energy into mechanical energy, or vice versa.

The processor is the central component of a computer or electronic device. The processor is responsible for executing instructions and controlling the other components of the system. The performance and capabilities of a device are largely determined by the speed and power of the processor.

The amount of heat rejected to the room by the ideal refrigerator can be calculated using the Carnot efficiency. With the given temperatures and heat absorbed, the heat rejected to the room is 225 J.

To calculate the amount of heat rejected to the room by the ideal refrigerator, we can use the Carnot efficiency, which is given by the formula:

Efficiency = 1 - ([tex]T_c_o_l_d[/tex] / [tex]T_h_o_t[/tex])

where[tex]T_c_o_l_d[/tex]is the temperature of the cold reservoir (freezer compartment) and [tex]T_h_o_t[/tex] is the temperature of the hot reservoir (room temperature).

Given:

[tex]T_c_o_l_d[/tex] = -9 °C (converted to Kelvin: 264 K)

[tex]T_h_o_t[/tex]= 25 °C (converted to Kelvin: 298 K)

Heat absorbed from the freezer compartment ([tex]Q_c_o_l_d[/tex] = 120 J

First, we calculate the Carnot efficiency:

Efficiency = 1 - (264 K / 298 K)

Efficiency ≈ 0.1134

The Carnot efficiency represents the ratio of heat transferred from the cold reservoir to the work done by the refrigerator. Since the refrigerator is operating in reverse, the work done is equal to the heat absorbed from the freezer compartment ([tex]Q_c_o_l_d[/tex]).

[tex]Q_c_o_l_d[/tex] = 120 J

Now, we can calculate the heat rejected to the room ([tex]Q_h_o_t[/tex]) using the equation:

[tex]Q_h_o_t[/tex] = Efficiency * [tex]Q_c_o_l_d[/tex]

[tex]Q_h_o_t[/tex] ≈ 0.1134 * 120 J

[tex]Q_h_o_t[/tex] ≈ 13.61 J

Therefore, the amount of heat rejected to the room by the ideal refrigerator is approximately 13.61 J.

For more such information on: heat

https://brainly.com/question/21406849

#SPJ8

The velocity of the third piece is (81.25 m/s, -43.3 m/s).

To determine the velocity of the third piece, we can use the principle of conservation of momentum.

Given:

Mass of the first piece (m1) = 150 kg

Velocity of the first piece (v1) = 150 m/s (to the East)

Mass of the second piece (m2) = 100 kg

Velocity of the second piece (v2) = 200 m/s at a direction of south 60° West

Let's break down the velocities into their respective horizontal (x) and vertical (y) components.

For the first piece:

v1x = 150 m/s (since it's moving to the East)

v1y = 0 m/s (no vertical component)

For the second piece:

v2x = 200 m/s * cos(60°) = 200 m/s * 0.5 = 100 m/s (horizontal component)

v2y = -200 m/s * sin(60°) = -200 m/s * 0.866 = -173.2 m/s (vertical component, negative since it's moving downward)

Now, let's calculate the momentum of the first and second pieces:

The momentum of the first piece (p1) = m1 * v1

= 150 kg * 150 m/s

= 22,500 kg·m/s

The momentum of the second piece (p2) = m2 * v2

= 100 kg * (100 m/s, -173.2 m/s)

= (10,000 kg·m/s, -17,320 kg·m/s)

To find the total momentum after the explosion, we can add the momenta of the individual pieces:

Total momentum after the explosion = p1 + p2

= (22,500 kg·m/s, 0 kg·m/s) + (10,000 kg·m/s, -17,320 kg·m/s)

= (32,500 kg·m/s, -17,320 kg·m/s)

The total momentum after the explosion should also be equal to the momentum of the third piece:

The momentum of the third piece (p3) = m3 * v3

Given:

Mass of the third piece (m3) = 400 kg (calculated from the given mass of the bomb)

Let's assume the velocity of the third piece is (v3x, v3y).

Therefore, we have the equation:

(32,500 kg·m/s, -17,320 kg·m/s) = 400 kg * (v3x, v3y)

By equating the x and y components separately, we can solve for the velocity components of the third piece:

32,500 kg·m/s = 400 kg * v3x

-17,320 kg·m/s = 400 kg * v3y

Solving these equations, we find:

v3x = 81.25 m/s

v3y = -43.3 m/s

Therefore, the velocity of the third piece is approximately (81.25 m/s, -43.3 m/s).

know more about velocity here:

https://brainly.com/question/80295

#SPJ8

The velocity of the third piece is v₃ = -12500 kg·m/s / m₃

The law of conservation of momentum states that the total momentum before the explosion is equal to the total momentum after the explosion.

velocity of the third piece =  v₃.

The total initial momentum before the explosion = 0

The total final momentum after the explosion= 0

Initial momentum = 0 kg·m/s (since the bomb is at rest)

Final momentum = m₁v₁ + m₂v₂ + m₃v₃

m₁ = mass of the first piece = 150 kg

v₁ = velocity of the first piece = 150 m/s (to the east)

m₂ = mass of the second piece = 100 kg

v₂ = velocity of the second piece = 200 m/s (south 60° west)

m₃ = mass of the third piece = unknown

v₃ = velocity of the third piece = unknown

0 = (150 kg)(150 m/s) + (100 kg)(200 m/s)(cos(60°)) + (m₃)(v₃)

final momentum = 0 and hence  v₃ is found as :

0 = 22500 kg·m/s - 10000 kg·m/s + (m₃)(v₃)

-12500 kg·m/s = (m₃)(v₃)

v₃ = -12500 kg·m/s / m₃

Learn more about law of conservation of momentum  at:

https://brainly.com/question/1113396

#SPJ1

The acceleration of the mass 2m is - (8/5) a θ´´.

We have two masses m and 2m connected by a string without slipping over a uniform circular pulley of mass 2m and radius a. We have to find the acceleration of the masses and write down the Lagrangian function and Lagrange's equation. The angular position of the pulley as generalized coordinate is used. Lagrangian function

L = T – VL = Kinetic energy - Potential energy

The kinetic energy is the sum of the kinetic energies of the two masses and the pulley. The potential energy is the sum of the potential energies of the two masses. The potential energy of the pulley can be ignored since it is fixed. Let θ be the angular position of the pulley, x be the distance fallen by the mass m and y be the distance fallen by the mass 2m.Kinetic energy of mass m (K1)K1 = ½ mv²where v = (dx/dt) is the velocity of mass mKinetic energy of mass 2m

(K2)K2 = ½ (2m) (dy/dt)²where (dy/dt) is the velocity of mass 2mKinetic energy of pulley (K3)The pulley is rolling without slipping, so the velocity of the point at the edge of the pulley is given byv = R(θ´)where R = a is the radius of the pulley. Hence, the kinetic energy of the pulley is

K3 = ½ I (θ´)²where I = (2/5) M R² = (2/5) (2m) a² is the moment of inertia of the pulleyPotential energy of mass m (V1)V1 = mgywhere g is the acceleration due to gravityPotential energy of mass 2m (V2)V2 = 2mgxThe Lagrangian function isL = K1 + K2 + K3 - V1 - V2L = ½ m(dx/dt)² + ½ (2m) (dy/dt)² + ½ (2/5) (2m) a² (θ´)² - mgy - 2mgxL = ½ m(dx/dt)² + ½ (2m) (dy/dt)² + ½ (4/5) ma² (θ´)² - mgy - 2mgxLagrange's

equationLet's find the equation of motion of the mass m using Lagrange's equation. The Lagrangian function depends on three variables, so we need three equations of motion.Lagrange's equation isd/dt (δL/δ(dx/dt)) - δL/δx = 0The first term gives usd/dt (δL/δ(dx/dt)) = m(dx/dt) + (4/5) ma² (θ´)(d/dt)(θ´) = m(dx²/dt²) + (4/5) ma² θ´´The second term gives usδL/δx = -d/dx (mgy) = 0The third term gives usδL/δ(θ) = d/dt (δL/δ(θ´))δL/δ(θ) = d/dt [(4/5) ma² (θ´)] = (4/5) ma² θ´´

The equation of motion ism(dx²/dt²) + (4/5) ma² θ´´ = 0We can solve this equation to find the acceleration of the mass m.The acceleration of the mass mThe acceleration of the mass m is given bya = dx²/dt² = - (4/5) a θ´´Therefore, the acceleration of the mass m is - (4/5) a θ´´.The equation of motion of the pulley is obtained in

the same way as above but we need to use the moment of inertia I of the pulley in the Lagrangian. We get(4/5) ma² θ´´ + 2mgRθ´² = 0Dividing by (4/5) ma², we getθ´´ + (5/8gR) θ´² = 0The acceleration of the mass 2m is given by the same expression as above but with m replaced by 2m.

For more question acceleration

https://brainly.com/question/460763

#SPJ8

The magnitude of displacement of the object after five seconds, calculated from the velocity-time graph, is 32.5 m. The correct answer is option E.

For more questions on the magnitude of displacement

https://brainly.com/question/26012010

#SPJ8

The height of the building is approximately 32.34 meters.

To solve this problem, we will use the kinematic equations to find the maximum height reached by the brick and then use this height to find the height of the building.

We can start by breaking the initial velocity of the brick into its horizontal and vertical components as follows:

v₀x = v₀cos(θ) = 17cos(25°) ≈ 15.84 m/s

v₀y = v₀sin(θ) = 17sin(25°) ≈ 7.23 m/s

where θ is the angle of the initial velocity to the horizontal.

Next, we can use the following kinematic equation to find the maximum height reached by the brick:

y = y₀ + v₀yt - 1/2gt²

where y₀ is the initial height (height of the building), t is the time of flight, and g is the acceleration due to gravity (9.81 m/s²).

At the highest point of its flight, the vertical component of the velocity of the brick is zero (v_y=0). We can use this fact to find the time taken to reach maximum height:

v_y = v₀y - gt

0 = v₀y - gt_max

t_max = v₀y / g ≈ 0.738 s

We can then substitute this value of t_max into the expression for y to obtain the maximum height:

y_max = y₀ + v₀y t_max - 1/2 g t_max²

where we set y = y_max and t = t_max.

Next, we can use the total flight time of the brick (3.1 s) to find the initial height of the building:

3.1 = t_max + t_down

where t_down is the time taken by the brick to fall from the maximum height to the ground. Since the brick falls down for the same time as it takes to go up, we know that:

t_down ≈ t_max ≈ 0.738 s

Substituting this value into the equation above, we find:

3.1 ≈ 2 × 0.738 s

Finally, we can use the value of y_max obtained earlier to calculate the height of the building:

y₀ = y_max - v₀y t_down + 1/2 g t_down²

y₀ = y_max - v₀y t_max + 1/2 g t_max²

y₀ ≈ 32.34 m

for more such questions on building

https://brainly.com/question/13677417

#SPJ8

a.  the tension in the rope is  91.5 N.

b.   the moment of inertia of the wheel is  0.1008 kg⋅m².

c.  the angular speed of the wheel 2.30 s after it begins rotating is  38.34 rad/s.

(a)

The tension in the rope can be found by considering the forces acting on the object.

ma = mg*sin(θ) - T

(14.0 kg)(2.00 m/s²)

= (14.0 kg)(9.8 m/s²)*sin(37°) - T

T = (14.0 kg)(9.8 m/s²)*sin(37°) - (14.0 kg)(2.00 m/s²)

T =  91.5 N

(b)

The moment of inertia of a wheel:

I = (1/2)MR²

I = (1/2)(14.0 kg)(0.12 m)²

I = 0.1008 kg⋅m²

(c)

The angular acceleration of the wheel:

α = a/R

α = angular acceleration,

a = linear acceleration of the object,

R =  radius of the wheel.

α = (2.00 m/s²)/(0.12 m)

α = 16.67 rad/s²

The angular speed (ω) of the wheel after time t is :

ω = ω₀ + αt

ω = 0 + (16.67 rad/s²)(2.30 s)

ω = 38.34 rad/s

Learn more about angular speed at:
https://brainly.com/question/25279049

#SPJ1

(a) The tension in the string is determined as 19.6 N.

(b) The acceleration of each object is 5.3 m/s².

(c) The distance each object will move in the first second if it started from rest is 2.65 m.

(a) The tension in the string is the resultant weight of the masses and magnitude is calculated as follows;

T = ( 5.7 kg - 3.7 kg ) x 9.8 m/s²

T = 19.6 N

(b) The acceleration of each object is calculated as follows;

a = T / m

where;

a = 19.6 N / 3.7 kg

a = 5.3 m/s²

(c) The distance each object will move in the first second if it started from rest is calculated as;

s = ut + ¹/₂at²

where;

s = 0 + ¹/₂(5.3)(1²)

s = 2.65 m

Learn more about acceleration here: https://brainly.com/question/14344386

#SPJ1

(a) The acceleration of the system is 8.5 m/s².

(b) The tension in the cord connecting the 4.0 kg and 1.0 kg blocks is 42.5 N.

(c) The force exerted by the 1.0 kg block on the 2.0 kg block is 59.5 N.

To solve this problem, we can use Newton's second law of motion (F = ma) and consider the forces acting on each block individually.

(a) Determine the acceleration given this system:

To find the acceleration (a) of the system, we can use the net force acting on the 4.0 kg block (m3). The only force acting on m3 is the applied force (F = 34 N).

F = m3 * a

34 N = 4.0 kg * a

Solving for a, we find:

a = 34 N / 4.0 kg

a = 8.5 m/s²

Therefore, the acceleration of the system is 8.5 m/s².

(b) Determine the tension in the cord connecting the 4.0-kg and the 1.0-kg blocks:

To find the tension in the cord (T), we can consider the forces acting on the 1.0 kg block (m1).

T - F = m1 * a

T - 34 N = 1.0 kg * 8.5 m/s²

T - 34 N = 8.5 N

T = 42.5 N

Therefore, the tension in the cord connecting the 4.0 kg and 1.0 kg blocks is 42.5 N.

(c) Determine the force exerted by the 1.0-kg block on the 2.0-kg block:

To find the force exerted by the 1.0 kg block (m1) on the 2.0 kg block (m2), we can consider the forces acting on the 2.0 kg block.

F - T = m2 * a

F - 42.5 N = 2.0 kg * 8.5 m/s²

F - 42.5 N = 17 N

F = 59.5 N

Therefore, the force exerted by the 1.0 kg block on the 2.0 kg block is 59.5 N.

for more questions on acceleration
https://brainly.com/question/460763
#SPJ8

Answer:

Approximately [tex]1.89\; {\rm m\cdot s^{-1}}[/tex].

Explanation:

Let [tex]m_{A}[/tex] and [tex]m_{B}[/tex] denote the mass of the two vehicles. Let [tex]u_{A}[/tex] and [tex]u_{B}[/tex] denote the velocity before the collision. Let [tex]v_{A}[/tex] and [tex]v_{B}[/tex] denote the velocity after the collision.

Since the collision is elastic, both momentum and kinetic energy should be conserved.

For momentum to conserve:

[tex]m_{A} \, v_{A} + m_{B} \, v_{B} = m_{A}\, u_{A} + m_{B}\, u_{B}[/tex].

For kinetic energy to conserve:

[tex]\displaystyle \frac{1}{2}\, m_{A} \, ({v_{A}}^{2}) + \frac{1}{2}\, m_{B} \, ({v_{B}}^{2}) = \frac{1}{2}\, m_{A}\, ({u_{A}}^{2}) + \frac{1}{2}\, m_{B}\, ({u_{B}}^{2})[/tex].

Simplify to obtain:

[tex]\displaystyle m_{A} \, ({v_{A}}^{2}) + m_{B} \, ({v_{B}}^{2}) = m_{A}\, ({u_{A}}^{2}) + m_{B}\, ({u_{B}}^{2})[/tex].

It is given that [tex]m_{A} = 282\; {\rm kg}[/tex], [tex]m_{B} = 210\; {\rm kg}[/tex], [tex]u_{A} = 2.82\; {\rm m\cdot s^{-1}}[/tex], and [tex]u_{B} = 1.72\; {\rm m\cdot s^{-1}}[/tex]. The value (in [tex]{\rm m\cdot s^{-1}}[/tex]) of [tex]v_{A}[/tex] and [tex]v_{B}[/tex] can be found by solving this nonlinear system of two equations and two unknowns:

[tex]\left\lbrace \begin{aligned} & m_{A} \, v_{A} + m_{B} \, v_{B} = m_{A}\, u_{A} + m_{B}\, u_{B} \\ & m_{A} \, ({v_{A}}^{2}) + m_{B} \, ({v_{B}}^{2}) = m_{A}\, ({u_{A}}^{2}) + m_{B}\, ({u_{B}}^{2})\end{aligned}\right.[/tex].

[tex]\left\lbrace \begin{aligned} & 282 \, v_{A} + 210 \, v_{B} = 282\, (2.82) + 210\, (1.72) \\ & 282 \, ({v_{A}}^{2}) + 210 \, ({v_{B}}^{2}) = 282\, ({2.82}^{2}) + 210\, ({1.72}^{2})\end{aligned}\right.[/tex].

Solving this system gives two possible sets of solutions:

However, the second set of solutions is invalid since it suggests that the velocity of the two vehicles stayed unchanged after the collision. Hence, only the first set of solutions ([tex]v_{A} &\approx 1.89\; {\rm m\cdot s^{-1}}[/tex], [tex]v_{B} &\approx 2.98\; {\rm m\cdot s^{-1}}[/tex]) is valid.

Therefore, the velocity of vehicle [tex]A[/tex] would be approximately [tex]1.89\; {\rm m\cdot s^{-1}}[/tex] after the collision.

(a) The speed at which the ball was launched is approximately 10.91 m/s.

(b) The ball clears the wall by approximately 1.50 m vertically.

(c) The horizontal distance from the wall to the point on the roof where the ball lands is approximately 24.02 m.

To solve this problem, we'll analyze the motion of the ball in two dimensions: horizontal and vertical.

(a) First, let's calculate the initial speed at which the ball was launched. We can use the time of flight and the horizontal distance traveled to find the initial horizontal velocity (Vx) of the ball.

The horizontal distance traveled by the ball (d) is given as 24.0 m, and the time of flight (t) is given as 2.20 s.

Using the equation for horizontal distance:

d = Vx * t

Rearranging the equation, we can solve for Vx:

Vx = d / t

Plugging in the known values:

Vx = 24.0 m / 2.20 s

Simplifying the equation, we find:

Vx ≈ 10.91 m/s

The initial horizontal velocity of the ball is approximately 10.91 m/s.

(b) Next, let's find the vertical distance by which the ball clears the wall. We can use the time of flight and the vertical motion of the ball to calculate this.

The vertical distance traveled by the ball is the difference between the height of the wall (h) and the height of the playground (hb).

Δy = h - hb

Plugging in the known values:

Δy = 7.40 m - 5.90 m

Simplifying the equation, we find:

Δy = 1.50 m

The ball clears the wall by approximately 1.50 m vertically.

(c) Finally, let's determine the horizontal distance from the wall to the point on the roof where the ball lands.

Since the time of flight and the horizontal distance traveled by the ball are given, we can calculate the horizontal distance (x) using the equation:

x = Vx * t

Plugging in the known values:

x = 10.91 m/s * 2.20 s

Simplifying the equation, we find:

x ≈ 24.02 m

The ball lands approximately 24.02 m horizontally from the wall on the roof.

for more questions on horizontal distance

https://brainly.com/question/25825784

#SPJ8

The six digit grid coordinates for the windtee  should be 3.

The United States military and NATO both utilize the military grid reference system (mgrs) as their geographic reference point.

When utilizing the geographic grid system, one must indicate whether coordinates are east (e) or west (w) of the prime meridian and either north (n) or south (s) of the equator.

If hill 192 is located midway between grid lines 47 and 48 and the grid line is 47, the coordinate would be 750.

Learn more about grid system at:

https://brainly.com/question/30159056

#SPJ1

The six digit grid coordinates for the windtee is determined as 100049.

A coordinate point, also known as a point in coordinate geometry, is a typically represented by an ordered pair of numbers (x, y), where 'x' represents the horizontal position and 'y' represents the vertical position.

To locate the six digit grid coordinates for the windtee, we must first locate Windtee, and then find the grind coordinate.

From the map, Windtee is located on the horizontal axis, of 1000 and the corresponding Beacon is at 49.

So the six digit grid coordinates = 100049.

Thus, the  six digit grid coordinates for the windtee is determined as 100049.

Learn more about coordinate points here: https://brainly.com/question/17206319

#SPJ1

In "The Argonauts," Robinson effectively utilizes language techniques such as metaphor, repetition, and sentence structure to develop his argument to his younger self and engage young readers in the present. Through these techniques, Robinson creates a powerful and relatable narrative that resonates with his audience.

Robinson employs metaphors to convey complex ideas in a compelling and accessible manner. For instance, he compares his struggle with identity and gender to the mythical journey of the Argonauts, making it relatable and captivating for young readers. This metaphorical language enables readers to grasp the profound emotions and challenges he faced during his own personal journey.

Repetition is another technique Robinson employs to reinforce key ideas and create a rhythmic and memorable reading experience. By repeating certain phrases or concepts, he emphasizes their significance and invites readers to reflect on them. This repetition serves to engage young readers by encouraging them to contemplate their own experiences and perspectives.

Furthermore, Robinson carefully structures his sentences to create a sense of rhythm and flow, enhancing the overall readability and impact of his argument. Short, concise sentences create moments of clarity and emphasis, while longer, more descriptive sentences evoke a contemplative and introspective tone. This varied sentence structure adds depth and nuance to his narrative, captivating young readers and keeping them engaged throughout.

In conclusion, through the effective use of metaphor, repetition, and sentence structure, Robinson engages and captivates young readers, inviting them to reflect on their own identities and experiences. His language choices not only develop his argument to his younger self but also establish a connection with present-day young readers, making his work both impactful and relatable.

for such more questions on techniques

https://brainly.com/question/12601776

#SPJ8

When white light reflects off of a green surface, only the green wavelengths of light are reflected (option d).

1. White light is a combination of all visible wavelengths of light, including red, orange, yellow, green, blue, indigo, and violet.

2. When white light hits a green surface, the surface absorbs some wavelengths of light and reflects others.

3. The color we perceive as "green" is the result of the green wavelengths of light being reflected by the surface.

4. In this case, the green surface absorbs all the wavelengths of light except for the green wavelengths, which are reflected back.

5. As a result, our eyes detect the reflected green light and interpret it as the color green.

6. This phenomenon occurs because the green surface selectively absorbs and reflects different wavelengths of light based on its molecular structure and the interactions between light and matter.

7. The absorption and reflection of specific wavelengths of light give objects their perceived color.

8. Therefore, when white light reflects off of a green surface, only the green wavelengths of light are reflected, while the other wavelengths are absorbed by the surface.

For more such questions on light, click on:

https://brainly.com/question/10728818

#SPJ8

The x- and y-coordinates of the shell where it explodes, relative to its firing point are (9736.5 m, 762.3 m) respectively.

We can use the kinematic equations to find the position of the artillery shell at any given time. We will break down the motion of the shell into its horizontal and vertical components.

First, we can find the initial horizontal and vertical velocities of the shell as follows:

\begin{align} v_{0x} &= v_0 \cos(\theta) = 300 \cos(52.0^\circ) \approx 192.9\text{ m/s}\ v_{0y} &= v_0 \sin(\theta) = 300 \sin(52.0^\circ) \approx 245.4\text{ m/s} \end{align}

We can use the vertical motion of the shell to find the time it takes to reach its maximum height, using the following kinematic equation:

$$y = v_{0y}t - \frac{1}{2}gt^2$$

At maximum height, the vertical velocity will be zero, so we can solve for the time it takes to reach this point:

\begin{align} 0 &= v_{0y}t - \frac{1}{2}gt^2\ t &= \frac{v_{0y}}{g} \approx 25.2\text{ s} \end{align}

Therefore, the time it takes for the shell to reach maximum height is 25.2 seconds. Using this time, we can find the maximum height, as follows:

\begin{align} y_\text{max} &= v_{0y}t - \frac{1}{2}gt^2\ &= 245.4\text{ m/s} \cdot 25.2\text{ s} - \frac{1}{2}(9.81\text{ m/s}^2)(25.2\text{ s})^2\ &\approx 762.3\text{ m} \end{align}

The time it takes for the shell to hit the mountainside can be found by solving for the time when y = 0:

\begin{align} 0 &= v_{0y}t - \frac{1}{2}gt^2\ t &= \frac{v_{0y} + \sqrt{(v_{0y})^2 + 2gy_\text{max}}}{g} \approx 50.5\text{ s} \end{align}

Therefore, the time it takes for the shell to hit the mountainside is 50.5 seconds. The x-coordinate of the explosion can be found by using the horizontal velocity and the time it takes for the shell to hit the mountainside:

\begin{align} x &= v_{0x}t\ &= 192.9\text{ m/s} \cdot 50.5\text{ s}\ &\approx 9736.5\text{ m} \end{align}

Therefore, the x-coordinate of the explosion is 9736.5 meters. The y-coordinate of the explosion is simply the height of the mountainside:

$$y = 0 + 762.3\text{ m} = 762.3\text{ m}$$

Therefore, the y-coordinate of the explosion is 762.3 meters.

for more such questions on explodes

https://brainly.com/question/31317998

#SPJ8

In this case, the demand (D1) moves to the left (D2), this also happens with supply (S1) leading to (S2), moreover, the intersections between these lines represent E1, E2, and E3.

Due to an increase in salary, it is expected the demand for dinners increase, which means this line would move to the left. This occurs as a higher wage for everyone implies people are more willing to pay for dinner than before.

This change would also mean restaurants are likely to provide more quantity, which increases the supply, and therefore in this process the equilibrium changes.

Learn more about demand in https://brainly.com/question/30402955

#SPJ1

Answer:

To solve this problem, we need to use some principles of physics, specifically Newton's second law (F=ma) and the equations of motion. Here are the steps:

1. Calculate the acceleration (a)

We can use the equation of motion to find the acceleration:

v_f^2 = v_i^2 + 2a*d

where:

v_f = final velocity = 6.80 m/s

v_i = initial velocity = 3.00 m/s

d = distance = 2/3 of the length of the fish = 2/3 * 1.50 m = 1.00 m

a = acceleration (which we are trying to find)

Rearranging the equation to solve for a gives us:

a = (v_f^2 - v_i^2) / (2*d)

2. Calculate the magnitude of the force F

Once we have the acceleration, we can use Newton's second law (F=ma) to calculate the force. The net force acting on the fish as it jumps out of the water is the difference between the upward force F exerted by the tail fin and the downward force due to gravity (mg). The net force is also equal to the product of the mass of the fish and its acceleration (ma). Therefore, we have:

F - mg = ma

Rearranging this equation to solve for F gives us:

F = ma + mg

Now let's plug in the numbers and do the calculations.

First, let's find the acceleration:

a = (v_f^2 - v_i^2) / (2*d)

a = (6.80 m/s)^2 - (3.00 m/s)^2) / (2*1.00 m)

a = (46.24 m^2/s^2 - 9.00 m^2/s^2) / 2 m

a = 37.24 m^2/s^2 / 2 m

a = 18.62 m/s^2

The salmon's acceleration is 18.62 m/s^2 upward.

Next, let's find the force F. We know the mass of the fish is 52.0 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So,

F = ma + mg

F = (52.0 kg)(18.62 m/s^2) + (52.0 kg)(9.8 m/s^2)

F = 969.24 N + 509.6 N

F = 1478.84 N

So, the magnitude of the force F exerted by the salmon's tail fin during this interval is approximately 1479 N.

a) The speed of the 6.00 kg block after descending 0.800 m is 2.07 m/s.

b) We cannot calculate the work done by the friction force.

c) The net work done on the system of two blocks during the 0.800 m downward displacement of the 6.00 kg block is 29.13 J. The work done by gravity is 47.04 J, the work done by friction is unknown, and the work done by the tension in the rope is zero.

(a) The work done on the 6.00 kg block by gravity can be calculated using the formula:

Work_gravity = force_gravity * displacement * cos(theta),

where force_gravity is the weight of the block, displacement is the downward displacement of the block, and theta is the angle between the force and displacement vectors (which is 0 degrees in this case).

The weight of the block is given by:

force_gravity = mass * acceleration_due_to_gravity = 6.00 kg * 9.8 m/s^2 = 58.8 N.

Plugging in the values, we get:

Work_gravity = 58.8 N * 0.800 m * cos(0) = 47.04 J.

The work done on the 6.00 kg block by the tension in the rope is given by:

Work_tension = tension * displacement * cos(theta).

Plugging in the values, we get:

Work_tension = 37.0 N * 0.800 m * cos(180) = -29.6 J.

The negative sign indicates that the tension is in the opposite direction of the displacement.

Using the work-energy theorem, we can find the speed of the 6.00 kg block after descending 0.800 m:

Work_net = change_in_kinetic_energy.

Since the block starts from rest, its initial kinetic energy is zero. Therefore:

Work_net = Final_kinetic_energy - Initial_kinetic_energy = 1/2 * mass * velocity^2.

Solving for velocity, we get:

velocity = sqrt(2 * Work_net / mass).

The net work done on the block is the sum of the work done by gravity and the tension:

Work_net = Work_gravity + Work_tension = 47.04 J - 29.6 J = 17.44 J.

Plugging in the values, we get:

velocity = sqrt(2 * 17.44 J / 6.00 kg) = 2.07 m/s.

Therefore, the speed of the 6.00 kg block after descending 0.800 m is 2.07 m/s.

(b) The total work done on the 8.00 kg block during the 0.800 m displacement can be calculated using the work-energy theorem:

Work_net = change_in_kinetic_energy.

Since the 8.00 kg block is not moving vertically, its initial and final kinetic energies are zero. Therefore:

Work_net = Final_kinetic_energy - Initial_kinetic_energy = 0.

The work done on the 8.00 kg block by the tension in the rope is given by:

Work_tension = tension * displacement * cos(theta).

Plugging in the values, we get:

Work_tension = 37.0 N * 0.800 m * cos(0) = 29.6 J.

The work done on the 8.00 kg block by the friction force can be calculated using the formula:

Work_friction = force_friction * displacement * cos(theta),

where force_friction is the frictional force on the block. However, the problem statement does not provide the value of the friction force. Therefore, we cannot calculate the work done by the friction force.

(c) The net work done on the system of two blocks during the 0.800 m displacement of the 6.00 kg block can be found using the work-energy theorem:

Work_net = change_in_kinetic_energy.

Since the system starts from rest, the initial kinetic energy of the system is zero. Therefore:

Work_net = Final_kinetic_energy - Initial_kinetic_energy = 1/2 * (6.00 kg + 8.00 kg) * velocity^2.

Simplifying, we get:

Work_net = 1/2 * 14.00 kg * velocity^2.

Using the value of velocity calculated in part (a), we get:

Work_net = 1/2 * 14.00 kg * (2.07 m/s)^2 = 29.13 J.

The work done on the system of two blocks by gravity is the sum of the work done on the individual blocks by gravity:

Work_gravity_system = Work_gravity_6kg + Work_gravity_8kg = 47.04 J + 0 J = 47.04 J.

The work done on the system of two blocks by the tension in the rope is the sum of the work done on the individual blocks by the tension:

Work_tension_system = Work_tension_6kg + Work_tension_8kg = -29.6 J + 29.6 J = 0 J.

Therefore, the net work done on the system of two blocks during the 0.800 m downward displacement of the 6.00 kg block is 29.13 J. The work done by gravity is 47.04 J, the work done by friction is unknown, and the work done by the tension in the rope is zero.

Note: The calculations for part (b) and (c) were based on the given information, but the value of the friction force was not provided in the problem statement.

For more such questions on work done, click on:

https://brainly.com/question/8119756

#SPJ8