Answer:
There are several basic ways to reduce sound: increasing the distance between source and receiver, decoupling, using noise barriers to reflect or absorb the energy of the sound waves, using damping structures such as sound baffles for absorption, or using active antinoise sound generators.
Why does strenuous activities make the heart beat faster?
Explanation:
When you exercise the muscles in your body must contract, in order to do that they need oxygen, glucose, a molecule called ATP, and amino acids. As your muscles use these compounds and contract themselves, they will create waste products like carbon dioxide, and lactic acid that must be carried away from the muscles. When exercising many muscles will all require nutrients and elimination of waste products constantly at the same time. To meet this demand the heart must rapidly increase the rate at which it beats and pushes blood through the body. This is why the heart beats significantly faster during exercise.
Q12. Calculate the resistance of a microwave with 5V and a current of 300mA
Answer:
To calculate the resistance of the microwave, we can use Ohm's Law, which states that:
resistance = voltage / current
Substituting the given values into this equation, we get:
resistance = 5V / 0.3A
resistance = 16.67 ohms
Therefore, the resistance of the microwave with 5V and a current of 300mA is 16.67 ohms.
please help me quick
Answer:40m East
Explanation:
A velocity vs. time graph is shown.
Velocity (m/s)
20
16
12
8
4
0
0
Velocity vs Time
1
2
3
Time (s)
4
5
What is the acceleration of the object?
0 m/s²
* 0.25 m/s²2
4 m/s²
8 m/s²
The acceleration of the object is - 4 m/s².
What is the acceleration of an object?
The acceleration of an object is the measure of change of velocity with change in time of motion.
Mathematically, the formula for acceleration is given as;
a = Δv / Δt
a = ( v₂ - v₁ ) / ( t₂ - t₁ )
where;
v₂ is the final velocityv₁ is the initial velocityt₂ is the final time of motiont₁ is the initial timeFrom the data given, we have;
velocity (m/s) time ( s )
20 1
16 2
12 3
8 4
4 5
a = ( 16 - 20 ) / ( 2 - 1 )
a = - 4 m/s²
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HELP NEEDED ASAP!!!
A crane is lifting a 13,700 N load from the ground to a height of 41.4 m. If this process takes 24.0 seconds, what is the power put out by the crane?
23,600 W
13,700 W
1190 W
570 W
Dividing this by 24.0 s gives a power output of 23,600 W.
What is power?Power is the ability to influence or control the behaviour of people, events, or things. It is the capacity to make decisions and take action in order to effect change. Power can be physical, economic, political, cultural, or social, and can be held by individuals, organizations, or governments. Power can be used positively to create positive change, or negatively to oppress or exploit. It can be used to create a sense of safety, stability, and justice, or to create uncertainty and chaos.
The power output of the crane is calculated by dividing the work done by the crane (the force multiplied by the distance moved) by the time taken to do the work. In this case, the work done is 13,700 N x 41.4 m = 570,380 Nm. Dividing this by 24.0 s gives a power output of 23,600 W.
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A ball is dropped from a height of 10m .At the same time, another ball is thrown vertically upward at an initial speed of 10m/sec .How high above the ground will the two ball collide?
The height the two balls will collide at 5.1 m above the ground after travelling for 1 second
Calculating the heights of the ball.Let's assume that the upward direction is positive, and the downward direction is negative. We can use the kinematic equations of motion to solve the problem.
For the ball that is dropped, we can use the equation:
y = y₀ + v₀t + 1/2 at²
Where:
y = final position (unknown)y₀ = initial position = 10mv₀ = initial velocity = 0 m/s (since it is dropped)a = acceleration due to gravity = -9.8 m/s² (negative since it is acting in the downward direction)t = time taken (unknown)Therefore, the equation becomes:
y = 10 + 0t - 1/2 (9.8)t²
For the ball that is thrown upward, we can use the equation:
y = y₀ + v₀t + 1/2 at²
where:
y = final position (unknown)y₀ = initial position = 0 mv₀ = initial velocity = 10 m/s (since it is thrown upward)a = acceleration due to gravity = -9.8 m/s² (negative since it is acting in the downward direction)t = time taken (unknown)Therefore, the equation becomes:
y = 0 + 10t - 1/2 (9.8) t²
Since both balls will collide at the same height, we can equate the two equations to solve for t and y.
10 - 1/2 (9.8) t² = 10t - 1/2 (9.8) t²
Simplifying the equation, we get:
10t = 10
t = 1 second
Substituting t = 1 second into either equation, we get:
y = 10 * (1) - 1/2 (9.8) * (1)²
y = 5.1 meters
Therefore, the two balls will collide at a height of 5.1 meters above the ground.
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The maximum acceleration is given as 0.2m/s2
A) find the velocity and
displacement of the train in 12s if it starts to speed up from rest.
B) How long will it take for this train to reach a velocity of 54km/ h if it continues to accelerate at the same rate?
A) the train's final velocity after 12 seconds of accelerating at 0.2 m/s^2 from rest is 2.4 m/s, and its displacement is 14.4 m.
B) it will take the train 75 seconds to reach a velocity of 54 km/h (15 m/s) if it continues to accelerate at the same rate of 0.2 m/s^2.
How The Train's acceleration was calculatedA) If the train starts from rest, its initial velocity is 0 m/s. Using the equation for constant acceleration, we can find the final velocity and displacement of the train after 12 seconds:
Final velocity = initial velocity + acceleration x time
Final velocity = 0 m/s + 0.2 m/s^2 x 12 s
Final velocity = 2.4 m/s
Displacement = (initial velocity x time) + (1/2 x acceleration x time^2)
Displacement = (0 m/s x 12 s) + (1/2 x 0.2 m/s^2 x (12 s)^2)
Displacement = 14.4 m
Therefore, the train's final velocity after 12 seconds of accelerating at 0.2 m/s^2 from rest is 2.4 m/s, and its displacement is 14.4 m.
B) First, we need to convert the final velocity to m/s:
54 km/h = 15 m/s (rounded to two decimal places)
Using the same equation for constant acceleration, we can solve for the time it takes for the train to reach a velocity of 15 m/s with an acceleration of 0.2 m/s^2:
Final velocity = initial velocity + acceleration x time
15 m/s = 0 m/s + 0.2 m/s^2 x time
time = 75 seconds
Therefore, it will take the train 75 seconds to reach a velocity of 54 km/h (15 m/s) if it continues to accelerate at the same rate of 0.2 m/s^2.
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Passengers experience a much smaller
decelleration in modern cars than they did
back in the 1970s. Why is that?
The modern and old cars are fantastic. But however they are different from one another. The vintage cars cannot compete with today's cars. The car engines are significantly advanced over the years.
What is deceleration?The deceleration refers to the acceleration in the direction opposite to the direction of the velocity. It always reduces the speed of the objects. The slowing down of a bike in a traffic is an example of deceleration.
The modern cars have smaller deceleration, because the engines in today's cars are more powerful and reliable. They provide greater safety, stability and efficiency. The fuel tank in the modern cars are also greater than the old cars.
Thus the Passengers experience a much smaller deceleration in modern cars.
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1. What is the wave speed of a wave that has a frequency of 1500 Hz and a wavelength of 0.50 m?
Answer:
750m/s
Explanation:
v = fλ = (1500 Hz)(0.5 m) = 750m/s
Answer:
0.5 m and 1500 Hz divided by 750 m/s equals 750 m/s.
Explanation:
Brainliest pls!
A hockey puck with a mass of 0.171 kg slides over the ice. The puck initially slides with a speed of 5.65 m/s, but it comes to a rough patch in the ice which slows it down to a speed of 3.05 m/s.
How much energy is dissipated as the puck slides over the rough patch?
To answer the question we have, 1.93401 J of energy is lost when the puck travels over the uneven surface.
What is the easiest way to define energy?Energy is referred to by scientists as the capacity for work. People have figured out how to transform energy from one kind to the other before employing it to accomplish tasks, making western civilisation possible.
Hockey weighs 0.171 kg.
Starting speed: 5.65 m/s
Ultimately, the speed was 3.05 m/s.
We must determine how much kinetic energy was lost on the tough patch.
[tex]E_{d}=\frac{1}{2} v^2_{2} -v^2_1[/tex]
Where, m = mass
v₁ = Initial velocity
v₂ = Final velocity
Put the value into the formula
[tex]E_{d}=\frac{1}{2}[/tex] × 0.171 × [tex](3.05^2 - 5.65^2)[/tex]
= 1.93401 J energy is dissipated as the puck slides over the rough patch.
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If a town installs new power lines in the middle of summer, what factor needs to be accommodated in their set up?
When a town puts in new power lines during the height of summer, it needs to be able to handle the increased electrical load on the power grid that will probably come from more people using air conditioners.
Summer is the hottest season in many parts of the world, so people rely a lot on air conditioning to keep their homes and businesses cool. As a result, the summer months typically see the greatest demand for electricity.When new power lines are installed, what upgrades are required?The power grid needs to be able to handle the increased demand for electricity that will result from the use of air conditioning when new power lines are installed. In order to guarantee that there is sufficient capacity to meet the increased demand, this may necessitate improvements to the existing infrastructure, which may include transformers, distribution lines, and substations.
In addition, it may be necessary to coordinate the installation of new power lines with the local utility company to avoid disrupting the existing power supply to homes and businesses. This may necessitate temporary power outages or other measures to guarantee that the installation goes off without a hitch and does not pose any safety risks.
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Exam Instructions
Question 8 of 20:
Select the best answer for the question
8. Which of the following is a healthy example of practicing self-care?
OA. Using junk food to cope with stress
OB. Spending extra hours working at the office
OC. Reflecting on a happy memory
OD. Avoiding friends and family for weeks
Mark for review (Will be highlighted on the review page)
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Self-care can be demonstrated in a healthy way by recalling a happy memory.
Is self-care included in reflection?The first step toward self-care is allowing yourself to be honest and vulnerable. Through self-reflection, you can at last let out all that you've been keeping down. Your journal is your very own private platform on which you can record your successes, anxieties, and worries.
What good examples of self-care do you have?Taking care of oneself exercises can go from proactive tasks, for example, practicing and practicing good eating habits, to mental exercises like perusing a book or rehearsing care, to otherworldly or social exercises, for example, imploring or getting lunch with a companion.
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Seismic waves, known as P – waves, and S – waves can be use to study the earths interior, which otherwise would have be been impossible to explore. Which properties of P Dash and S – waves allow the study of earths interior.
(Multiple choice)
A. They travel at varying speeds, depending on the composition of layer.
B. They deflected while passing through layers of different compositions.
C. They are produced during earthquakes and volcanic eruptions.
D S – waves cannot pass through a layer of liquid composition
Gulag Dam, Yahtzee Dam, and Jinka Rhina Dam have 3 different heights as described in the table below.
Dam Height (m)
Gulag 132
Yahtzee 147
Jinka Rhina 181
Which dam has the ability to produce the most electricity, based only on height?
A. The Gulag because the dam has a shorter drop and the water will have the most potential energy to transfer to the turbine.
B. The Yahtzee because the drop at this height will have the most kinetic energy to transfer to the turbine.
C. The Jinka Rhina because the dam has the largest drop and the water produces the most kinetic energy to transfer to the turbine.
D. It is impossible to determine based on the data in the table.
The correct answer is D. The height of a dam is only one of many factors that determine its ability to produce electricity. Other important factors include the volume of water that can be held in the reservoir, the flow rate of the water, and the efficiency of the power generation equipment. Therefore, it is impossible to determine which dam has the ability to produce the most electricity based solely on its height.
A cyclist starts from rest and coasts down a 4.5 degree hill. The mass of the cyclist plus bicycle is 80 kg. The cyclist has traveled 260 m.
a) What was the net work done by gravity on the cyclist? (in J)
Express your answer using two significant figures.
b) How fast is the cyclist going? Ignore air resistance. (m/s)
Express your answer using two significant figures.
A block of mass 1.0 kg rests on a horizontal surface. The frictional coefficients for the block and surface are μs=0.50 and μk=0.40. (a) What is the minimum horizontal force required to move the block? (b) What is the block’s acceleration when this force is applied?
The 25N is the minimum horizontal force required to move the block, 20N force is applied.
What is mass ?The amount of matter in a body is referred to as its mass. The kilograms is the kilograms, which is the SI unit of mass (kg). Mass is defined as: Mass = Density/Volume.
What is force ?A body can change its state of rest or motion when an external force acts on it. It is directed and has a magnitude.
Therefore, 25N is the minimum horizontal force required to move the block, 20N force is applied.
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1. A fairground ride consists of a large vertical drum that spins so
fast that everyone inside it stays pinned against the wall when
the floor drops away. The diameter of the drum is 10 m. Assume
that the coefficient of static friction between the drum and the
rider's clothes is 0.15.
a) What is the minimum speed required for the riders so that
they stay pinned against the inside of the drum when the
floor drops away?
b) What is the angular velocity of the drum at this speed?
a) Minimum speed required for the riders so that they stay pinned against the inside of the drum is 18m/s.
b) Angular velocity of the drum at this speed having diameter of the drum is 10 m is 3.6 rad/s
What is Friction ?Friction is a resistance to motion of the object. for example, when a body slides on horizontal surface in positive x direction, it has friction in negative x direction and that measure of friction is a frictional force.
frictional force is directly proportional to the Normal(N).
i.e. [tex]F_{fri}[/tex] ∝ N
[tex]F_{fri}[/tex] = μN
where μ is called as coefficient of the friction. It is a dimensionless quantity.
When a body is kept on horizontal surface, its normal will be straight upward which is reaction of mg. i.e. N=mg.
Given,
Diameter of the drum D = 10m , Radius r = 5m
Coefficient of static friction = 0.15
a) To stay everyone pinned against the wall of drum. Frictional Force must be equal to weight mg which are opposite to each other.
μN = mg ........1)
Centrifugal acceleration = Normal
mv²÷r = N
With this equation 1 becomes
μ[tex]\frac{mv^{2} }{r}[/tex] = mg
v² = rg÷μ
v² = 5m*9.8m/s ÷ 0.15
v² = 326.6
v= [tex]\sqrt{326.6}[/tex] = 18.07 ~ 18 m/s
Hence minimum speed required for the riders is 18m/s.
b) for angular velocity of the drum, V=rω
ω = v÷r
ω = 18m/s ÷ 5m
ω = 3.6 rad/s
hence angular velocity of the drum at 18m/s speed is 3.6 rad/s
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An astronomer wants to calculate the magnitude of gravitational acceleration at the surface of a newly discovered exoplanet (an exoplanet is a planet orbiting a star other than our sun). The astronomer has estimated the mass of the exoplanet to be 1.01 times the mass of Earth, and the radius of the planet to be 0.99 times the radius of Earth.
The magnitude of gravitational acceleration at the surface of a newly discovered exoplanet, having the mass to be 1.01 times the mass of Earth, and the radius of the planet to be 0.99 times the radius of Earth is 10.06 m/s².
What is gravitational acceleration?The acceleration that an object experiences when gravity is the only force acting on it is known as gravitational acceleration.
In an empty space, all bodies accelerate at the same rate, regardless of their masses or compositions. This means that any two objects falling from the same height would always hit the ground at the same time if there was no air friction.
Depending on altitude, latitude, and longitude, this free-fall acceleration can range from 9.764 to 9.834 m/s² over the surface of the Earth. However, the accepted standard value is 9.80665 m/s². Gravity anomalies are the regions where this value dramatically varies.
According to the formula,
g = [tex]\frac{GM}{R^{2} }[/tex]
where,
g is gravitational acceleration
G is gravitational constant,
M is mass of planet and,
R is the radius of the planet.
G = 6.67 × 10⁻¹¹
M = 1.01 × 6 × 10²⁴ kg
R = 0.99 × 6.4 × 10⁶ m
substituting the values and solving for g,
g = 10.06 m/s²
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The mass of the object with kinetic energy of 43200 Joules and velocity of 23 m/s will be 163.33 Kg.
What is Kinetic energy?Kinetic energy is the energy of an object which is present due to the state of motion of the object. Kinetic energy depends upon the mass and velocity of the object. The SI unit of Kinetic energy is meter per second square (m/s²).
KE = 1/2 mv²
where, KE is the Kinetic energy,
m is the mass of the object,
v is the velocity of the object.
KE = 43200 Joules,
v = 23 m/s
KE = 1/2 mv²
m = 2 KE/ v²
m = 2 × 43200/ 23 × 23
m = 86400/ 529
m = 163.33 kg
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using F=MA, if you weighed 375N what would your mass be *have to show work*
Answer:
38.22 kg
Explanation:
To use the formula F=ma to find the mass of an object, we need to know the force acting on it and its acceleration. In this case, the force acting on the object is its weight, which we can find using the equation:
weight = mass x acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.81 m/s^2. Therefore, we can write:
weight = mass x 9.81 m/s^2
We are given that the weight of the object is 375 N. Substituting this value into the equation, we get:
375 N = mass x 9.81 m/s^2
To solve for mass, we need to isolate it on one side of the equation. We can do this by dividing both sides by 9.81 m/s^2:
mass = 375 N / 9.81 m/s^2
Using a calculator, we can evaluate this expression to get:
mass = 38.22 kg
Therefore, if an object weighs 375 N, its mass is approximately 38.22 kg on Earth.
If 2 particles are in phase that means they have the exact same pattern of _______________.
Answer:the shape
Explanation:
Answer:
oscillation Explanation: If two particles having the same phase it must either two consecutive troughs or two consecutive crests.What is the wavelength (in nm) of maximum intensity for a celestial body with a temperature of 50000 K?
The wavelength of maximum intensity for a celestial body with a temperature of 50000 K is approximately 577 nm.
What is wavelength?To find the wavelength of maximum intensity for a celestial body with a temperature of 50000 K, we can use Wien's displacement law, which relates the temperature of an object to the wavelength at which it emits the most radiation. The law is given by:
λ_max = b / T
where λ_max is the wavelength of maximum intensity, b is Wien's displacement constant (2.898 × 10⁻³ m·K), and T is the temperature in Kelvin.
We can convert the temperature of 50000 K to Kelvin by adding 273.15 to get:
T = 50000 K + 273.15 = 50273.15 K
Plugging in the values, we get:
λ_max = (2.898 × 10⁻³ m·K) / 50273.15 K
Simplifying, we get:
λ_max = 5.77 × 10⁻⁸ meters
To convert meters to nanometers, we can multiply by 10⁹:
λ_max = 5.77 × 10⁻⁸ meters × 10⁹ nm/m = 577 nm
Therefore, the wavelength of maximum intensity for a celestial body with a temperature of 50000 K is approximately 577 nm.
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which of the following is an example of uniform acceleration
motion under force
motion under gravity
motion under power
none
The following is example of uniform acceleration, that is : motion under force.
What is uniform acceleration?Uniform acceleration refers to constant rate of change in velocity, which means that acceleration of an object is constant over time. Motion under force can result in uniform acceleration if the force is constant and object is free to move in straight line.
Motion under gravity and motion under power can both result in acceleration but they are not necessarily uniform. For example, object falling under gravity experiences constantly increasing acceleration due to increasing speed and gravitational force acting on it, which means acceleration is not uniform.
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What is the time if the velocity is 294 ft/s and the acceleration is 22 ft/s²?
If the velocity is 294 ft/s and the acceleration is 22 ft/[tex]s^{2}[/tex], the time will be 13.36 s.
Given,
Final velocity, v = 294 ft/s
acceleration, a = 22 ft/[tex]s^{2}[/tex]
According to the first equation of motion
v = u + at
Where u = initial velocity
and t = time
To find out time (t) we will use the first equation of motion as
v = u + at
or, t = [tex]\frac{v-u}{a}[/tex]
where u = 0 ft/s
So, t = [tex]\frac{294-0}{22}[/tex]
= 13.36 s
Hence, the time will be 13.36 s.
A positive point charge Q1= 2.6×10−5 C is fixed at the origin of coordinates, and a negative point charge Q2= −5.1×10−6 C is fixed to the x axis at x=+2.0m.
Find the location of the place along the x axis where the electric field due to these two charges is zero. (the location should be (x) m from Q2
The location at the point where electric field becomes zero is at 3.6m, when a positive point charge Q1= 2.6×10−5 C is fixed at the origin and a negative point charge Q2= −5.1×10−6 C is fixed at 2.0m.
What is electric field ?Electric field is field around electrically charged particle where columbic force of attraction or repulsion can be experienced by other charged particles. It is denoted by letter E and it's SI unit is V/m Volt per meter or N/C newton per coulomb.
Electric field comes inward to the center of the negative charge and it is going outward for positive charge.
Given,
Q₁= 2.6×10⁻⁵ C
Q₂= −5.1×10⁻⁶ C
x = 2.0m,
In this case there are two charges, one at the origin and other is at 2m distance from origin. Both these charges are kept along positive x axis. looking at the situation there are 2 cases
Case 1 ( electric field in between two charges)
in this case direction of the resultant electric field in between two charges is along positive x direction (direction of electric field of positive charge is outward along x axis which is along positive x direction and direction of electric field of negative charge is inward along x axis which is also in positive x direction).
Case 2 ( right side of the negative charge)
In this case direction of electric field of positive charge is outward along x axis which is along positive x direction and direction of electric field of negative charge is inward along x axis but which is in opposite direction of electric field due to positive charge.
Hence our electric field is zero at right side of the negative charge.
on right side, electric fields due to both charges are opposite to each other then we can write mathematically E₁ - E₂ = 0 at the point where resultant electric field is zero. Where E₁ is elctric field due to positive charge and E₂ is electric field due to negative charge.
E₁ - E₂ = 0
E₁ = E₂
[tex]\frac{kQ_{1}}{x^{2}} = \frac{kQ_{2} }{(x+2)^{2}}[/tex]
[tex]\frac{Q_{1}}{x^{2}} = \frac{Q_{2} }{(x+2)^{2}}[/tex]
[tex]\frac{Q_{1}}{Q_{2} }} = \frac{x^{2} }{(x+2)^{2}}[/tex]
(2.6×10⁻⁵ C ÷ -5.1×10⁻⁶ C) [tex]= \frac{x^{2} }{(x+2)^{2}}[/tex]
[tex]\frac{x^{2} }{(x+2)^{2}}[/tex] = 5.098 ≅ -5.1
x² = 5.1 (x+2)²
x = 2.25(x+2)
x=2.25x + 4.5
x(1-2.25) = 4.5
x(-1.25) = 4.5
x = 3.6m
Hence Electric field is zero at 3.6m from origin.
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Answer:
0.0312J
Explanation:
Given:
Relaxed length of the spring (L0) = 0.115 mSpring constant (k) = 51.0 N/mExtended length of the spring (L) = 0.150 mWant: Elastic potential energy stored in the spring
Solve:
The elastic potential energy stored in the spring can be calculated using the following formula:
Elastic potential energy = 0.5 * k * (L - L0)^2
Substituting the given values into the equation:
Elastic potential energy = 0.5 * 51.0 N/m * (0.150 m - 0.115 m)^2
Elastic potential energy = 0.5 * 51.0 N/m * (0.035 m)^2
Elastic potential energy = 0.5 * 51.0 N/m * 0.001225 m^2
Elastic potential energy = 0.0312 J
Therefore, the elastic potential energy stored in the spring when its length is 0.150 m is 0.0312 J.
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The total distance traveled by the skier is 160 m.
option C.
What is distance?Distance is a measure of how far apart two objects or points are. It can be defined as the numerical value of the physical space between two objects or points.
Distance can be measured in a variety of units, such as meters, feet, miles, or kilometers, depending on the system of measurement used.
Distance can also refer to the length of a path between two points, which can be a straight line or a curved line.
The total distance traveled by the skier is calculated as follows;
total distance = distance ( 0 min) + distance (1 min) + distance (2 min) + distance ( 3 mins)
total distance = 0 m + (120 m - 0 m) + ( 160 m - 120 m )
total distance = 0 m + 120 m + 40 m = 160 m
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What is a type of potential energy that a marshmallow has if the marshmallow is sitting in the bag
Answer:
potential until moved than kinetic
Explanation:
A ballast bag is dropped from a balloon that is 300 m above the ground and rising at 13 m/s. For the bag, find (a) the maximum height reached, (b) its position and velocity 5.0 s after it is released, and (c) the time at which it hits the ground.
a. The maximum height reached by the ballast bag is approximately 300 m + 8.45 m = 308.45 m.
b. 5.0 s after it is released, the ballast bag is at a height of approximately 177.5 m above the ground, and its velocity is approximately -36.5 m/s
c. The ballast bag hits the ground approximately 18.1 s after it is released.
(a) To find the maximum height reached by the bag, we can use the kinematic equation:
v_f^2 = v_i^2 + 2aΔy
where v_f is the final velocity (which is zero at the maximum height), a is the acceleration due to gravity (approximately -9.8 m/s^2), and Δy is the change in height.
Rearranging and solving for Δy, we get:
Δy = v_i^2 / (2a) = (13 m/s)^2 / (2*(-9.8 m/s^2)) ≈ 8.45 m
Therefore, the maximum height reached by the ballast bag is approximately 300 m + 8.45 m = 308.45 m.
(b) To find the position and velocity of the bag 5.0 s after it is released, we can use the equations:
y = y_i + v_it + (1/2)at^2
v_f = v_i + at
where y_i is the initial height (300 m), v_i is the initial velocity (13 m/s), t is the time elapsed (5.0 s), and a is the acceleration due to gravity (-9.8 m/s^2).
Using these equations, we can find:
y = 300 m + 13 m/s*(5.0 s) + (1/2)(-9.8 m/s^2)(5.0 s)^2 ≈ 177.5 m
v_f = 13 m/s + (-9.8 m/s^2)*(5.0 s) ≈ -36.5 m/s
Therefore, 5.0 s after it is released, the ballast bag is at a height of approximately 177.5 m above the ground, and its velocity is approximately -36.5 m/s (i.e., it is moving downward).
(c) To find the time at which the ballast bag hits the ground, we can use the equation:
y = y_i + v_i*t + (1/2)at^2
Setting y = 0 (since the ground is at y = 0), y_i = 300 m, v_i = 13 m/s, and a = -9.8 m/s^2, we get:
0 = 300 m + 13 m/st + (1/2)(-9.8 m/s^2)*t^2
Rearranging and solving for t using the quadratic formula, we get:
t = (-13 ± sqrt(13^2 - 4*(-4.9)(300))) / (2(-4.9))
The positive solution is the time at which the ballast bag hits the ground:
t ≈ 18.1 s
Therefore, the ballast bag hits the ground approximately 18.1 s after it is released.
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