Given data:
Force;
[tex]F=200\text{ N}[/tex]Stretching;
[tex]\begin{gathered} x=27\text{ cm} \\ =0.27\text{ m} \end{gathered}[/tex]The force is given as,
[tex]F=kx[/tex]Here, k is the force constant.
The expression for the force constant is given as,
[tex]k=\frac{F}{x}[/tex]Substituting all known values,
[tex]\begin{gathered} k=\frac{200\text{ N}}{0.27\text{ m}} \\ =740.74\text{ N/m} \end{gathered}[/tex]Therefore, the force constant of the spring is 740.74 N/m. Hence, option (3); 740 N/m is the best choice.
what is the direction of the resultant? ASAPPP
Answer: The direction of the resultant can be determined by finding the angle that the resultant makes with either the north-south or the east-west vector. The diagram at the right shows the angle theta (Θ) marked inside the vector addition triangle. This angle theta is the angle that the resultant makes with west.
Explanation: Hope this helps.
A 50.0-g Super Ball traveling at 28.5 m/s bounces off a brick wall and rebounds at 18.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 4.00 m/s,what is the magnitude of the average acceleration of the ball during this time interval?m/s
Given data:
*The given mass of the Superball is m = 5.0 g
*The initial speed of the Superball is u = -28.5 m/s
*The ball rebounds at a final speed is v = +18.0 m/s
*The given time is
[tex]t=4.00ms=4.00\times10^{-3}\text{ s}[/tex]Considering the rebound direction is positive
The formula for the magnitude of the average acceleration of the ball during this time interval is given as
[tex]a_{avg}=\frac{v-u}{t}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} a_{avg}=\frac{18.0-(-28.5)}{(4.0\times10^{-3})} \\ =11625m/s^2 \end{gathered}[/tex]A circus van moves 50 km [E] in the first hour, 40 km [W] in the second hour, and 30 km [N] in the next half hour. Calculate the average velocity of the travelling circus van?
The average velocity of the travelling circus van is 12.64km/h.
As we already know, the directions east[E] and west[W] are opposite to each other, north[N] perpendicular to both of them.
We know, average velocity V,
V = total displacement/total time taken
Let us assume the situation on a coordinate plane, and say that the van started from origin,
The circus van first goes to the east direction and travels 50Km. After that, it travels 40Km back,
So, he travels straight 50Km and then return back 40Km, so now, his current position is 10Km in the east direction,
Now, from the point in 10km east, he travels 30km north,
Now, his current and final position is 10km east and 30km north,
His initial position was 0km in east and 0km in north,
So, his total displacement D is,
D² = (10)²+(30)²
D² = 100+900
D² = 1000
D = 10√10 Km.
Total time T taken by him is,
T = 1+1+.05
T = 2.5 hours,
Putting the values, the average velocity V is,
V = D/T
V = 10√10/2.5
V= 12.64 km/h
So, the average velocity is 12.64km/h.
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A penny is dropped from a building and it takes 7.00 seconds to hit the ground.
What was the penny’s final velocity as it hit the ground?
The final velocity of the pen as it hits the ground is 68.6 meters per seconds.
What is the velocity of the pen as it hits the ground?Velocity is simply the speed at which an object moves in a particular direction.
From the first equation of motion
v = u + gt
Where v is final velocity, u is initial velocity, t is time elapsed and g is acceleration due to gravity ( g = 9.8m/s² )
Given the data in the question;
The pen was initially at rest before the drop, Initial velocity u = 0Elapsed time t = 7.00sFinal velocity v = ?To determine the velocity just before the pen hits the ground, plug the values into the formula and solve for v.
v = u + gt
v = 0 + ( 9.8m/s² × 7.00s )
v = 9.8m/s² × 7.00s
v = 68.6m/s
Therefore, the final velocity is 68.6 meters per seconds.
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What is the kinetic energy of a 200 kg object that is moving at a velocity of 15 m/s?3000 Jb30,0000 Jc215 Jd2150 J
22500 Joules
Explanation
Kinetic energy is a form of energy that an object or a particle has by reason of its motion and mass ,
[tex]E_k=\frac{1}{2}mv^2[/tex]
where m is the mass of the object and v the velocity
Step 1
a)Let
[tex]\begin{gathered} m=200\text{ Kg} \\ v=15\frac{m}{s} \end{gathered}[/tex]now, replace
[tex]\begin{gathered} E_k=\frac{1}{2}mv^2 \\ E_k=\frac{1}{2}(200\text{ kg\rparen\lparen15}\frac{m}{s})^2 \\ E_k=\frac{1}{2}*45000\text{ Joules} \\ E_k=22500\text{ Joules} \end{gathered}[/tex]so, the answer is 22500 Joules
I hope this helps you
A child pushes, with a constant force, a merry-go-round with a radius of 3 m, from rest toan angular velocity of 4 Rad/s. What is the merry-go-round's centripetal acceleration atthis point?
The centripetal acceleration is given by:
[tex]a=\omega^2r[/tex]where ω is the angular velocity and r is the radius. In this case the angular velocity is 4 rad/s and the radius is 3 m; plugging these values we have:
[tex]\begin{gathered} a=(4^2)(3) \\ a=48 \end{gathered}[/tex]Therefore, the centripetal acceleration is 48 meters per second per second.
Scientific laws tell us what we can expect under certain circumstances, but what do they fail to explain?
OA. when
OB. why
OC. where
O D.
A certain transformer doubles input voltage. If the primary coil has 10 A of current, then the current in the
secondary coil is
O 25 A.
O 5 A.
O none of the above
O 2A.
O 10 A.
According to the given statement then the current in the secondary coil is 5A.
The correct option is B.
What does secondary coil in transformer do?Transformers have at least two windings or coils, as seen in the experiment above. The primary is referred to as such, and the secondary as such. AC electricity enters the primary coil here. Where the current is induced to carry out any sort of energy transfer is in the secondary coil.
Briefing:According to the question,
Current in primary coil, I[tex]_i_n[/tex] = 10A
Power = V[tex]_i_n[/tex]I[tex]_i_n[/tex] = V[tex]_o_u_t[/tex]I[tex]_o_u_t[/tex]
Then
By substituting the values,
V[tex]_i_n[/tex]* 10 =V[tex]_i_n[/tex]I[tex]_o_u_t[/tex]
By applying cross-multiplication,
10 = 2I[tex]_o_u_t[/tex]
I[tex]_o_u_t[/tex] = 10/2
= 5A
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The complete question is -
A certain transformer doubles input voltage. If the primary coil has 10 A of current, then the current in the secondary coil is
A- 25 A.
B- 5 A.
C- none of the above
D- 2A.
E- 10 A.
If the size of an object is 5.0 cm, and the size of the image formed by a lens is 15.0 cm, what is the magnification of the system?
The magnification of the system is 3.
To calculate the magnification, use the following system: magnification = the height of the photograph ÷ via the peak of the object. Plug your records into the formula and remedy. if your solution is more than 1, that means the photo is magnified. in case our solution is between zero and 1, the image is smaller than the object.
magnification = height of imagect/height of objest
= 15 cm/5 cm
= 3.
A magnification of one (plus or minus) approach that the image is the equal size as the object. If m has a value extra than 1 the photograph is greater than the item, and if an m with significantly much less than 1 way the photo is smaller than the item.
A negative magnification shows that the photograph is inverted. If the object is positioned in the direction of a converging lens than the focal period, the rays on the far side of the lens diverge. by means of extrapolating those traces returned (the red traces) the location of the digital image can be observed.
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Please help me
how law of motion applied in tug of war game need step by step explanation
Newtons law- For every action, there is a reaction
The first team to tug is the action force, causing the pull on the rope, as the reaction force, the other team's rope end feels the pull.
When two teams are pulling in opposite directions, the movement of the rope (as calculated by Newton's second law) will be determined by the net force on the rope.
Which of the following statements are correct?A.gamma rays travel faster than x-rays B.red light has a higher frequency than violet light C.Ultraviolet light and infrared light have the same frequency D.radio waves travel at the same speed as gamma rays
(A). The gamma rays and x-rays are the electromagnetic rays. The speed of the electromagnetic rays is constant.
[tex]c=3\times10^8ms^{-1}[/tex]Thus, the gamma rays and x-rays have the same speed.
Hence, option A is incorrect.
(B). The wavelength of the red light is larger than the wavelength of the violet light.
The frequency of light in terms of the wavelength is,
[tex]f=\frac{c}{\lambda}[/tex]where f is the frequency, c is the speed of light and
[tex]\lambda\text{ is the wavelength}[/tex]As the frequency is inversely propotional to the wavelength of light.
For the larger value of wavelength, the value of frequency is smaller and for the smaller value of the wavelength, the value of frequency is larger.
Thus, the frequency of the red light is smaller than the frequency of the violet light.
Hence, option B is incorrect.
(C). The ultraviolet light and infrared light have different value of wavelength.
Thus, the value of the frequency is not same for both the l
In most electric generators, either the armature (the coil of wire) or the magneticfield is ____ generating a(n) __---a) interrupted; impulse changeOb) nonconducting; flux lineOc) turned off; temporary dipoled) rotated; induced current
Answer:
d) rotated; induced current
Explanation:
MetalDensity in g/cm3Aluminum2.7Silver10.5Gold19.3Steel7.8Juan finds a foreign coin that is so dirty that he can't tell what it is made of.He knows the density of these common materials and decides to find out ifthe coin is made of one of the materials. The mass of the coin is about 12 g,and the volume is about 4 cm. Which type of material could it be?O A. SteelKB. GoldOC. AluminumD. Silver
To determine the material we will determine the density using the values of mass and volume. We will use the following formula:
[tex]\rho=\frac{m}{V}[/tex]Where:
[tex]\begin{gathered} \rho=\text{ density} \\ m=\text{ mass} \\ V=\text{ volume} \end{gathered}[/tex]Now, we plug in the values:
[tex]\rho=\frac{12g}{4cm^3}[/tex]Solving the operations:
[tex]\rho=3\text{ g/}cm^3[/tex]The closest material is the one with a density of:
[tex]\rho=2.7\text{ g/}cm^3[/tex]Therefore, the material could be aluminum.
Use this for the day before the day of your work
The given equation is:
[tex]\frac{1}{2}mv^2+mgh=E[/tex]Note that:
The mass m is constant
Total energy E is constant
The derivative of a constant is zero
g = 9.81 m/s^2
dh/dt = v
Compute d/dt of both sides
[tex]\begin{gathered} \frac{d}{dt}(\frac{1}{2}mv^2)+\frac{d}{dt}(mgh)=\frac{dE}{dt} \\ \\ \frac{1}{2}m\frac{d}{dt}(v^2)+mg\frac{dh}{dt}=0 \\ \\ \frac{1}{2}(m)(2v)\frac{dv}{dt}+mgv=0 \\ \\ mv\frac{dv}{dt}+mgv=0 \\ \\ mv\frac{dv}{dt}+9.81mv=0 \\ \\ mv(\frac{dv}{dt}+9.81)=0 \\ \\ \frac{dv}{dt}+9.81=0 \\ \\ \frac{dv}{dt}=-9.81\text{ m/s}^2 \end{gathered}[/tex]When a ball is dropped from a rooftop, it might make sense to choose the ground or the release point as the origin of the frame of reference. How do these choices make relevant calculations easier?
A reference point is a location or object that is used for comparison to determine whether or not something is moving. If an object changes position relative to a reference point, it is in motion. Buildings, trees, and signs that are fixed relative to Earth serve as good reference points.
How do you determine a frame of reference?To fully define a reference frame in n dimensions, n + 1 reference points are sufficient. A reference frame can be defined using rectangular Cartesian coordinates, with a reference point at the origin and a reference point one unit distance along each of the n coordinate axes.The ball's motion is independent of the reference frame and is consistent across reference frames.A reference point is a location or object that is used for comparison to determine whether or not something is moving. If an object changes position relative to a reference point, it is in motion. Buildings, trees, and signs that are fixed relative to Earth serve as good reference points.To learn more about : Reference frame
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how much power is delivered by the acting force over the first 6 s period?
Answer:
6 watts
Explanation:
Power is defined as
Power = Work done / time taken
Now in our case the work done is
W = F * d
For the first 6 meters, the work done is ( the area under the graph )
W = 6 * 6 = 36
Now assuming that this work was done in 6 seconds, the power delivered by the acting force is
W / t = 36 / 6 = 6 Watts
Hence the answer is 6 Watts.
Newer vehicles are designed with crumple zones at the front and rear ends. Crumplezones consist of materials that deform more easily than the other regions of the car.The purpose of these zones is to increase the safety of the passengers in case of acollision. Which statement correctly explains how crumple zones reduce the impactof a collision?They extend the distance over which the impact force slows the car's motion.They convert the nature of the collision from more inelastic to more elastic.They reduce the total momentum of the system involving the colliding vehicle.They increase the mass of the vehicle relative to that of other involved objects.
They extend the distance over which the impact force slows down the car's motion
Explanations:The essence of the crumpling zone in newer cars is to convert part of the Kinetic energy of the car into a controlled deformation.
This will reduce the motion of the car at impact so that it takes a considerably longer time to stop, extend the distance over which the impact force slows down the car's motion, and reduce the shock on the passengers. This is essentially because the impact force will be reduced
A physics text book has a mass of 2.2kg What is the weight on the earth
Given data
*The given mass of the physics textbook is m = 2.2 kg
*The value of the acceleration due to gravity is g = 9.8 m/s^2
The formula for the weight of the book on the earth is given as
[tex]W=mg[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} W=(2.2)(9.8) \\ =21.56\text{ N} \end{gathered}[/tex]Note: Fig
The figure above shows the forces exerted on a block that is sliding on a rough horizontal surface: The weight of the block is 500 N, the normal force is 500 N, the frictional force is 100 N, and there is an unknown force F exerted to the right. The acceleration of the block is .4m/s^2. The value of F is most nearly
A) 20 N
B) 80 N
C) 110 N
D) 120 N
The force 'F' on the block is equal to 120 N. Therefore, option D is correct.
What is frictional force?The frictional force is described as the force formed by two surfaces that slide against each other. The frictional force is affected by the texture of the surface, the angle, as well as the position of the object.
Friction can be defined as the force that resists motion when one surface comes in contact with the other surface. The mechanical advantage will reduce by the force of friction therefore the ratio of output to input will be reduced because of friction.
The formula of the frictional force can be represented as:
F = μmg
Given, the weight of the block, W = 500 N
W = mg
500 = m × 9.8
m = 51 Kg
The acceleration of the block, a = 0.4 m/s²
The frictional force of the block, F = 100 N
F(net) = F (applied) - F (frictional)
ma = F - 100
51 ×0.4 = F - 100
F = 100 + 20.4
F = 120.4 N
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In a head-on collision, a car stops in 0.14 s from a speed of 17.6 m/s. The driver has a mass of 70 kg, and is, fortunately, tightly strapped into his
seat. What is the magnitude of the average force applied to the driver by his seat belt during that fraction of a second? Round to two decimal places and express the answer in Sl units.
The rate at which an object's velocity with respect to time changes is known as its acceleration. Accelerations are vector quantities. The direction of the net force acting on an object determines its acceleration.
Velocity is the rate at which an object is changing position as perceived from a certain point of view and as measured by a particular unit of time. It is defined as the direction at which an object is traveling.
acceleration = (Velocity f - Velocity i) / time
= - 17.6 / 0.14 m/s
= - 125.714 m/s
A force is an influence that has the power to change an object's motion. A force can cause an object with mass to move at a different speed or accelerate. A push or a pull makes natural sense to describe force. Forces have both magnitude and direction because they are vector quantities.
Force = mass x acceleration
= 70 x (- 125.714 m/s) N
= - 8800 N
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6) Find the speed a spherical raindrop would attain by falling from 4.00 km. Do this:a) In the absence of air dragb) In the presence of air dragc) Assume that the diameter of the drop is 3 mm and the density of the water is 0.98x10^3 kg/m^3
We are asked to determine the velocity of a rain drop if it falls from 4 km.
To do that we will use the following formula:
[tex]2ah=v_f^2-v_0^2[/tex]Where:
[tex]\begin{gathered} a=\text{ acceleration} \\ h=\text{ height} \\ v_f,v_0=\text{ final and initial velocity} \end{gathered}[/tex]If we assume the initial velocity to be 0 we get:
[tex]2ah=v_f^2[/tex]The acceleration is the acceleration due to gravity:
[tex]2gh=v_f^2[/tex]Now, we take the square root to both sides:
[tex]\sqrt{2gh}=v_f[/tex]Now, we substitute the values:
[tex]\sqrt{2(9.8\frac{m}{s^2})(4000m)}=v_f[/tex]solving the operations:
[tex]280\frac{m}{s}=v[/tex]Therefore, the velocity without air drag is 280 m/s.
Part B. we are asked to determine the velocity if there is air drag. To do that we will use the following formula:
[tex]F_d=\frac{1}{2}C\rho_{air}Av^2[/tex]Where:
[tex]\begin{gathered} F_d=drag\text{ force} \\ C=\text{ constant} \\ \rho_{air}=\text{ density of air} \\ A=\text{ area} \\ v=\text{ velocity} \end{gathered}[/tex]We need to determine the drag force. To do that we will use the following free-body diagram:
Since the velocity that the raindrop reaches is the terminal velocity and its a constant velocity this means that the acceleration is zero and therefore the forces are balanced:
[tex]F_d=mg[/tex]Now, we determine the mass of the raindrop using the following formula:
[tex]m=\rho_{water}V[/tex]Where:
[tex]\begin{gathered} \rho_{water}=\text{ density of water} \\ V=\text{ volume} \end{gathered}[/tex]The volume is the volume of a sphere, therefore:
[tex]m=\rho_{water}(\frac{4}{3}\pi r^3)[/tex]Since the diameter of the raindrop is 3 millimeters, the radius is 1.5 mm or 0.0015 meters. Substituting we get:
[tex]m=(0.98\times10^3\frac{kg}{m^3})(\frac{4}{3}\pi(0.0015m)^3)[/tex]Solving the operations:
[tex]m=1.39\times10^{-5}kg[/tex]Now, we substitute the values in the formula for the drag force:
[tex]F_d=(1.39\times10^{-5}kg)(9.8\frac{m}{s^2})[/tex]Solving the operations:
[tex]F_d=1.36\times10^{-4}N[/tex]Now, we substitute in the formula:
[tex]1.36\times10^{-4}N=\frac{1}{2}C\rho_{air}Av^2[/tex]Now, we solve for the velocity:
[tex]\frac{1.36\times10^{-4}N}{\frac{1}{2}C\rho_{air}A}=v^2[/tex]Now, we substitute the values. We will use the area of a circle:
[tex]\frac{1.36\times10^{-4}N}{\frac{1}{2}(0.45)(1.21\frac{kg}{m^3})(\pi r^2)}=v^2[/tex]Substituting the radius:
[tex]\frac{1.36\cdot10^{-4}N}{\frac{1}{2}(0.45)(1.21\frac{kg}{m^{3}})(\pi(0.0015m)^2)}=v^2[/tex]Solving the operations:
[tex]70.67\frac{m^2}{s^2}=v^2[/tex]Now, we take the square root to both sides:
[tex]\begin{gathered} \sqrt{70.67\frac{m^2}{s^2}}=v \\ \\ 8.4\frac{m}{s}=v \\ \end{gathered}[/tex]Therefore, the velocity is 8.4 m/s
A point charge of −3μC is locatedat the center of a sphere with a radius r=5cm. What is the net electric flux through the surface?short answer pls asap
Given:
The total charge enclosed by the surface of the sphere, q=-3 μC
The radius of the sphere, r=5 cm=5×10⁻² m
To find:
The net electric flux through the surface of the sphere.
Explanation:
From Gauss's law, the net electric flux through the surface of the sphere is given by,
[tex]\phi=\frac{Q}{\epsilon_0}[/tex]Where ε₀ is the permittivity of free space.
On substituting the known values,
[tex]\begin{gathered} \phi=-\frac{3\times10^{-6}}{8.85\times10^{-12}} \\ =339\times10^3\text{ Nm}^2\text{/C} \end{gathered}[/tex]Final answer:
The net flux through the surface of the sphere is 339×10³ Nm²/C
analyze the motion of an object that has an acceleration of 0 m/s2
The soccer player ran 50 yards in 5.1 seconds speed,acceleration,velocity
With the initial velocity of 0 m/s the final velocity will be 17.54 m/s and the acceleration will be 3.84yards/s².
What is Newton's law of motion?
Newton gave three laws of motion which can be utilized to find the velocity, acceleration and displacement of a body. These laws are only applicable for constant acceleration.
What is deacceleration in physics?
deacceleration is a physical quantity that refers to the change of velocity per unit time it decreases the velocity of the object also known as deacceleration.
given:
initial velocity of soccer player = 0 m/s
distance covered by the soccer player= 50 yards
time taken by the soccer player = 5.1 seconds
using newtons second law of motion:
i.e.
s = u × t + 0.5 × a × t²
here,
s is displacement
u is initial velocity
v is final velocity
a is constant acceleration
t is the time taken
substituting value in newtons second law of motion we get,
50 = 0 + 0.5×5.1×5.1×a
a = 3.44 yards/s²
using newtons first law of motion we get,
v = u + a × t
final velocity = 0 + 3.44×5.1
final velocity = 17.54m/s
therefore, with the initial velocity of 0 m/s the final velocity will be 17.54 m/s and the acceleration will be 3.84yards/s².
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14. Most solids are good conductors of energy because their molecules...Select one:a. are close together and can easily transfer energy.b. are usually far apart and must transfer energy by convection.c. move slow so they make contact long enough to transfer energy. d. none of the above.
a) are close together and can easily transfer energy
Explanation:Note that:
• Molecules of a solid are strongly attached to each other and are tightly bound
,• The electrons of the solids are delocalized, and are able to move freely
,• The presence of the free moving electrons due to closeness of the molecules is responsible for the good conduction of solids
Most solids are good conductors of energy because their molecules are close together and can easily transfer energy
An inclined plane makes an angle of 30 degrees above the horizontal. If a block of 7 kg rests on the incline, what is the magnitude of the normal force that the incline exerts on the block?
Given data
*The given mass of the block is m = 7 kg
*The given angle is
[tex]\theta=30^0[/tex]The formula for the magnitude of the normal force that the inclined plane exerts on the block is given as
[tex]f_n=mg\cos \theta[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} f_n=(7)(9.8)\cos 30^0 \\ =59.41\text{ N} \end{gathered}[/tex]Hence, the magnitude of the normal force that the inclined plane exerts on the block is F_n = 59.41 N
A weight is suspended
with a rope and hangs freely. In what direction is the tension on the rope?
A. Parallel to the rope
B. Perpendicular to the rope
The force of tension is always directed Parallel to the rope and away from the mass attached.
What is Tension?Tension is a contact force that transfers by means of string or cable or, similar objects when a mass is hanged vertically by it.
Given is a weight that is suspended with a rope and hangs freely.
The Force of Tension always acts away from the mass that is hanged by it. Refer to the figure attached it will give a clear explanation of the Tension force. Since the mass is at rest, then for the mathematical analysis, we can write -
T = mg
The force of tension is equal to the weight of the mass. Talking about direction, the force of tension acts along the rope or parallel to the rope and away from the mass.
Therefore, we can say that the force of tension is always directed Parallel to the rope.
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Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The amounts she spent in each category are pictured here.Food - 267Rent - 333Other - 400Fun - 200What percent of her total spending did she spend on Rent? Round your answer to the nearest whole percent
Kara spending on food $267.
Spending on rent $333.
Spending on other things $400.
Spending on fun $200.
Her total expenditure;
[tex]\begin{gathered} \text{ total expenditure}=\text{ \$267}+\text{ \$333}+\text{ \$400}+\text{ \$200} \\ =\text{ \$1200} \end{gathered}[/tex]Percentage of her total spending on rent can be calculated as,
[tex]\begin{gathered} P=\frac{\text{ spending on rent}}{\text{ total expenditure}}\times100\text{ \%} \\ =\frac{\text{ \$333}}{\text{ \$1200}}\times100\text{ \%} \\ =27.75\text{ \%} \\ \approx28\text{ \%} \end{gathered}[/tex]Therefore, the percentage of total spending she spends on rent is about 28%.
What acceleration is needed to bring a car that is initially going 65.0 mi/hr to a complete stop in a distance of 57.0 m?
7.41 m/s^2
ExplanationWhen an object is traveling in a straight line with an increase or decrease in velocity at equal intervals of time, then the object is said to be in uniform acceleration
to find the acceleration we can use the formulas
[tex]\begin{gathered} x=v_it+\frac{1}{2}at^2 \\ and \\ v_f=v_1+at \end{gathered}[/tex]so
Step 1
a)
let
[tex]\begin{gathered} initial\text{ velocity}=v_i=65\frac{mi}{h} \\ final\text{ velocity= 0 \lparen complete stop-rest\rparen} \\ distance=57\text{ m=0.0354182 miles} \end{gathered}[/tex]b) replace in equation (2)
[tex]\begin{gathered} v_{f}=v_{1}+at \\ 0=65+at \\ -65=at \\ a=-\frac{65}{t} \end{gathered}[/tex]replace in equation (1)
[tex]\begin{gathered} x=v_{i}t+\frac{1}{2}at^{2} \\ 0.0354182=65t+\frac{1}{2}(-\frac{65}{t})t^2 \\ 0.0354182=65t-\frac{1}{2}(\frac{65}{})t^ \\ 0.0354182=65t-\frac{65}{2}t \\ 0.0354182=t(65-\frac{65}{2}) \\ 0.0354182=t(32.5) \\ t=\frac{0.0354182}{32.5}=0.001089\text{ hours} \end{gathered}[/tex]now, replace in the previous equation to find a
[tex]\begin{gathered} a=-\frac{65}{t} \\ a=-\frac{65\frac{mi}{h}}{0.001089\text{ hours }} \\ a=-59687\text{ }\frac{miles}{hour^2} \end{gathered}[/tex]so, the answer is
[tex]a=-59687.78\frac{m\imaginaryI les}{hour^{2}}[/tex]finally, let's convert the acceleration from miles per squared hour into meters per square second
remember that:
[tex]\begin{gathered} 1\text{ hour = 3600 seconds } \\ 1\text{ miles=1609.34 meters} \end{gathered}[/tex]so
[tex]\begin{gathered} a=-59,687\frac{m\imaginaryI les}{hour^{2}}(\frac{1\text{ hour}}{3600\text{ s}})^2(\frac{1609.34\text{ m}}{1\text{ mile}}) \\ a=-59,687\frac{\text{m}\mathrm{i}\text{les}}{\text{hour\textasciicircum{\text{2}}}}*\frac{1\text{ hour}^2}{12960000\text{s}^2}*(\frac{1609.34\text{ m}}{1\text{ mile}}) \\ a=-7.41\text{ }\frac{m}{s^2} \end{gathered}[/tex]hence
the acceleration is -7.41 m/s^2
I hope this helps you
Find the image distance of an object placed 3.00 cm in front of a convex mirror whose focal length is 8.00 cm.
Here,
object distance(u)= - 3.00cm;
focal length (f)= -8.00cm
object distance(v)= ?
Using lens formula
[tex]\begin{gathered} \frac{1}{f}\text{ = }\frac{1}{u}\text{ + }\frac{1}{v};\text{ } \\ \frac{1}{8.00}\text{ = }\frac{1}{3.00}\text{ +}\frac{1}{v}; \\ \therefore\frac{1}{v}=\text{ }\frac{1}{8}\text{ -}\frac{1}{3}=\text{ - }\frac{5}{24} \\ \therefore v=-\frac{24}{5}\text{ = -4.8 cm} \end{gathered}[/tex]Note: Here object is placed between focus and pole of the mirror as
u< f. Therefore a real and inverted image will be formed in same side that of object . So image distance have negative sigh according to sign convention.
Final answer is - 4.8 cm
As an object placed 3.00 cm in front of a convex mirror whose focal length is 8.00 cm, the image distance (di) is -24/5 cm.
The mirror equation can be used to determine the image distance (di) of an object put in front of a convex mirror:
1/f = 1/do + 1/di
Here,
f = focal length of the mirror
do = object distance
di = image distance
It is given that
Focal length = 8.00 cm
Object distance = 3.00 cm
So,
1/8.00 = 1/3.00 + 1/di
1/di = 1/8.00 - 1/3.00
1/di = (3 - 8)/(3*8) = -5/24
di = -24/5
Thus, the image distance (di) is -24/5 cm.
For more details regarding convex mirror, visit:
https://brainly.com/question/3627454
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