In order to slow down, a driver applies a force of 3130 N to their car's brakes for a distance of 14 m. The initial energy of the car is 100,000 J, what is the car's final energy​

Answers

Answer 1

The final energy of the car, given that the driver applied a force of 3130 N to the car's brake for a distance of 14 m is 43820 J

How do I determine the final energy of the car?

We'll begin by listing out the parameters given from the question. This is shown below:

Force applied = 3130 Ndistance travelled = 14 mInitial energy = 100000 JFinal energy =?

We know that energy is the ability to do work. Now, considering the given parameters from the question, we can obtain the final energy of the car as illustrated below:

Final energy = Force applied × distance travelled

Final energy = 3130 × 14

Final energy = 43820 J

Thus, from the calculation made above, we can conclude that the final energy of the car is 43820 J

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Related Questions

What conclusion can you draw from the information shown in this figure?

The speed of sound varies with the material in which the waves travel.

Sound waves can move more quickly through liquids than through solids.

Sound intensity is greater in water than in air.

The frequency of sound increases with wave speed.

What conclusion can you draw from the information shown in this figure?The speed of sound varies with

Answers

Answer:

The speed of sound varies with the material in which the waves travel.

Explanation:

knowledge and research

It can be concluded as per the given table that the speed of sound varies with the material in which the waves travel. The correct option is A.

What is speed?

Speed is the pace at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

It has a dimension of time-distance. As a result, the fundamental unit of time and the basic unit of distance are combined to form the SI unit of speed. Thus, the metre per second (m/s) is the SI unit of speed.

According to the given table, it can be inferred that the material in which the waves travel affects the speed of sound.

Thus, the correct option is A.

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PLEASE HELP
A problem says a plane is accelerating
3.42 m/s2 northeast. Which one of these
tables includes that information correctly?

PLEASE HELPA problem says a plane is accelerating3.42 m/s2 northeast. Which one of thesetables includes

Answers

Answer:

The answer is C, I just guessed and got it right lol

Explanation:

PLZZ ANSWER THE QUESTION ​

PLZZ ANSWER THE QUESTION

Answers

Answer:

D. ? Its the only one talking about color

If one oscillation has 3.0 times the energy of a second one of equal frequency and mass, what is the ratio of their amplitudes?

Answers

The ratio of their amplitudes is 3.

The relation between energy and amplitude is as follows:

\(E_{1} = \frac{1}{2} KA_{1} ^{2}\)

\(E_{2} =\frac{1}{2} KA_{2} ^{2}\)

As, we know , one oscillation has 3.0 times the energy of a second one of equal frequency and mass i.e.,

\(E_{1} = 3E_{2}\)

So, \(\frac{1}{2} KA_{1} ^{2} = 3(\frac{1}{2}KA_{2} ^{2} )\)

\(A_{1} ^{2} = 3A_{2} ^{2}\)

\(\frac{A_{1}^{2} }{A_{2}^{2} } = 3\)

Therefore,  the ratio of their amplitudes is 3.

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A train whistle is heard at 300 Hz as the train approaches town. The train cuts its speed in half as it nears the station, and the sound of the whistle is then 290 Hz. What is the speed of the train before and after slowing down? Assume the speed of sound is 343 m/s.

Answers

Answer:

The speed of the train before and after slowing down is 22.12 m/s and 11.06 m/s, respectively.

Explanation:

We can calculate the speed of the train using the Doppler equation:

\( f = f_{0}\frac{v + v_{o}}{v - v_{s}} \)        

Where:

f₀: is the emitted frequency

f: is the frequency heard by the observer  

v: is the speed of the sound = 343 m/s

\( v_{o}\): is the speed of the observer = 0 (it is heard in the town)

\( v_{s}\): is the speed of the source =?

The frequency of the train before slowing down is given by:

\( f_{b} = f_{0}\frac{v}{v - v_{s_{b}}} \)  (1)                  

Now, the frequency of the train after slowing down is:

\( f_{a} = f_{0}\frac{v}{v - v_{s_{a}}} \)   (2)  

Dividing equation (1) by (2) we have:

\( \frac{f_{b}}{f_{a}} = \frac{f_{0}\frac{v}{v - v_{s_{b}}}}{f_{0}\frac{v}{v - v_{s_{a}}}} \)

\( \frac{f_{b}}{f_{a}} = \frac{v - v_{s_{a}}}{v - v_{s_{b}}} \)   (3)  

Also, we know that the speed of the train when it is slowing down is half the initial speed so:

\( v_{s_{b}} = 2v_{s_{a}} \)     (4)

Now, by entering equation (4) into (3) we have:

\( \frac{f_{b}}{f_{a}} = \frac{v - v_{s_{a}}}{v - 2v_{s_{a}}} \)  

\( \frac{300 Hz}{290 Hz} = \frac{343 m/s - v_{s_{a}}}{343 m/s - 2v_{s_{a}}} \)

By solving the above equation for \(v_{s_{a}}\) we can find the speed of the train after slowing down:

\( v_{s_{a}} = 11.06 m/s \)

Finally, the speed of the train before slowing down is:

\( v_{s_{b}} = 11.06 m/s*2 = 22.12 m/s \)

Therefore, the speed of the train before and after slowing down is 22.12 m/s and 11.06 m/s, respectively.                        

I hope it helps you!                                                        

Which equation describes the sum of the vectors plotted below?​

Which equation describes the sum of the vectors plotted below?

Answers

The  equation describes the sum of the vectors plotted below is: \(\vec{r} = 4 \vec{x}+2 \vec{y}\)

What is vector quantity?

A physical quantity that has both directions and magnitude is referred to as a vector quantity.

A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.

According to the final position of the vector as shown in the figure, The final x co-ordinate is 4 and  the final y co-ordinate is 2.

the  equation describes the sum of the vectors plotted below is: \(\vec{r} = 4 \vec{x}+2 \vec{y}\)

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What holds the metal ions together in a lattice?
A. covalent bonds
B. metallic bonds
C. hydrogen bonds
D. ionic bonds

Answers

Metallic bonds! Hope this helps!! :))

Answer:

B. Metallic bonds.

HELP right awayyy !!!

HELP right awayyy !!!

Answers

Answer:

Question 4 is actually Acceleration

4 is actually acceleration

what is the most effortless walking speed for a person with 90cm long legs if the length of each step is 90cm​

Answers

Answer:

75 cm/second.

Explanation:

Formula:

Walking speed = stride length / time per step

Walking speed = 90cm/time per step

                         = 90cm/1.2 seconds (a common estimate time per step)

                         = 75cm/second.

An archer shoots an arrow over flat ground. The speed of the arrow is 45m/s. A.) What is the maximum possible range of the arrow? B.) At this range, what is the maximum height? C.) What 2 angles will give a range of 90 meters?

Answers

the answer is 80 degrees so simple try solving again


True or false. The planet's speed never changes. That is why we have a stable orbit.
O True
O False

Answers

This answer is true the earth always stays at one speed

A 10,000kg space ship is orbiting the moon with a radius of 25km from the ship to the center of the moon. It's tangential speed is 125m/s. What is the ships centripetal acceleration?

Is this the correct set-up for this problem.

ac=10,000kg(125m/s)2/25,000m

True or False?

Answers

Answer:

False

Explanation:

ac = v^2/r

acceleration is not dependent on the mass of the orbiting object.

Two blocks, 1 and 2, are connected by a massless string that passes over a massless pulley. 1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. 2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105

. The figure illustrates the configuration.

A system of two blocks connected by a rope passing over a pulley. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle. Box M subscript 1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M sub 1 and the surface is mu subscript 1. Box M subscript 2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle. The coefficient of friction between box M sub 2 and the surface is mu subscript 2.

Answers

The force acting on the system of two blocks connected by a rope passing over a pulley is -13.26 N.

The system of two blocks connected by a rope passing over a pulley are M1 and M2, where M1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M1 and the surface is mu subscript 1. M2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle.

The coefficient of friction between box M2 and the surface is mu subscript 2. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle.M1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. M2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105.The free-body diagram of M1 shows that the weight of M1 acts straight downwards (vertically) and the normal force acts perpendicular to the slope.

The force of friction opposes the motion and acts opposite to the direction of motion.M1 = 2.25 kgTheta subscript 1 = 42.5 degreesMu subscript 1 = 0.205g = 9.81 m/s²In the free-body diagram of M2, the normal force acts perpendicular to the incline of the slope, the weight of the object acts vertically downwards and parallel to the incline, and the force of friction opposes the motion and acts opposite to the direction of motion.M2 = 5.55 kgTheta subscript 2 = 33.5 degreesMu subscript 2 = 0.105g = 9.81 m/s²The tension in the string is the same throughout the rope. Since the masses are being pulled by the same rope, the acceleration of the objects is the same as the acceleration of the rope.

The tension in the string is directly proportional to the acceleration of the objects and the rope.A system of two blocks connected by a rope passing over a pulley has a total mass of M. The acceleration of the system is given by the formula below:a = [(m1-m2)gsin(θ1) - μ1(m1+m2)gcos(θ1)] / (m1 + m2)Where, μ1 = 0.205 is the coefficient of friction of block M1θ1 = 42.5 degrees is the angle of the incline of block M1M1 = 2.25 kg is the mass of block M1M2 = 5.55 kg is the mass of block M2g = 9.81 m/s² is the acceleration due to gravitysinθ1 = sin 42.5 = 0.67cosθ1 = cos 42.5 = 0.75The acceleration of the system is:a = [(2.25-5.55)(9.81)(0.67) - (0.205)(2.25+5.55)(9.81)(0.75)] / (2.25 + 5.55)a = -1.7 m/s² (the negative sign indicates that the system is accelerating in the opposite direction).

The force acting on the system is given by:F = MaWhere M is the total mass of the system and a is the acceleration of the system. The total mass of the system is:M = m1 + m2M = 2.25 + 5.55M = 7.8 kgThe force acting on the system is:F = 7.8(-1.7)F = -13.26 N (the negative sign indicates that the force is acting in the opposite direction).

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plz help me with hw A bus of mass 1000 kg moving with a speed of 90km/hr stops after 6 sec by applying brakes then calculate the distance travelled and amount of force applied.​

Answers

Answer:

Mass, M = 1000 kg

Speed, v = 90 km/h = 25 m/s

time, t = 6 sec.

Distance:

\({ \tt{distance = speed \times time }} \\ { \tt{distance = 25 \times 6}} \\ { \tt{distance = 150 \: m}}\)

Force:

\({ \tt{force = mass \times acceleration}} \\ { \bf{but \: for \: acceleration : }} \\ from \: second \: equation \: of \: motion : \\ { \bf{s = ut + \frac{1}{2} {at}^{2} }} \\ \\ { \tt{150 = (0 \times 6) + ( \frac{1}{2} \times a \times {6}^{2} ) }} \\ \\ { \tt{acceleration = 8.33 \: {ms}^{ - 2} }} \\ \\ { \tt{force = 1000 \times 8.33}} \\ { \tt{force = 8333.3 \: newtons}}\)

A sample of vegetable oil with density 913 kg/m3 is found to have a mass of 0.0365 kg. Find the volume of this sample

Answers

The volume of the vegetable oil is  0.00003998 m³.

The density of vegetable oil,

ρ = 913 kg/m³

The mass of vegetable oil,

m = 0.0365 kg

To find: The volume of the vegetable oil, V Solution: The density of any substance is defined as the mass of the substance per unit volume.

The formula for density is:

ρ = m/V

where, ρ is the density of the substancem is the mass of the substance V is the volume of the substance We can rearrange the above formula to find the volume of the substance:

V = m/ρSubstituting the given values of mass and density in the above formula,

We get:

V = 0.0365 kg / 913 kg/m³ = 0.00003998 m³ (approx)

Therefore, the volume of the vegetable oil is approximately 0.00003998 m³.

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Guys pls I need help with this question anyone plsss help it will be appreciated

Guys pls I need help with this question anyone plsss help it will be appreciated

Answers

Answer:

I think it is A.

Explanation:

Word has a meaning similar to obesity?

Fatness

Best definition for corpulence.

The state of being fat

A condition characterized by abnormal or excessive fat accumulation.

Treatable by a medical professional

Does diagnosis require lab test or imaging?

Doesn't require lab test or imaging

Time taken for recovery

Can last several years or be lifelong

Condition Highlight

Family history may increase likelihood for some types

One type of BB gun uses a spring driven plunger to blow the BB from its barrel. Calculate the force constant of its plunger's spring if you must compress it 0.150 m to drive the 0.0500 kg plunger to a top speed of 20.0 m/s.

Answers

Answer:

a) 889 N / m

b) 133 N

a runner runs 10 miles in 1 hour. how far could they run in 2 hours in m/s?
16000 m/hr
1500 km/s
8.88 m/s
4.44m/s

Answers

Answer:

4.47 m/s.

Explanation:

distance traveled, d = 10 miles

time, t = 1 hour

Speed of the runner, v = d / t

Speed of the runner = 10 miles / 1

Speed of the runner = 10 mph

1 mph ----------------------- 0.44704 m/s

10 mph -----------------------?

= 4.47 m/s

Thus, in 2 hours the distance traveled will change but the speed it still 10 mph or 4.47 m/s.

If a runner runs 10 miles in 1 hour, the runner will go 4.47m/s.

HOW TO CALCULATE DISTANCE?

The average speed of a moving body can be calculated using the following formula:

Average speed = distance/time

In 2 hours, the runner will run in 10 × 2 = 20 miles, which is equivalent to 10miles/hr

Next, we convert miles/hr to m/s as follows:

10miles/hr to 4.47m/s.

Therefore, runner runs 10 miles in 1 hour, the runner will go 4.47m/s.

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Compare the velocities of the meteorite and the bowling ball. By how many times is the velocity of the meteorite greater than the velocity of the ball?

Answers

Answer:

The velocity of the bowling ball (Vb) is 1,423.93 meters/second. The velocity of the meteorite (Vm) is 35 kilometers/second, which is equal to 35,000 meters/second.

To compare the two velocities, divide the larger quantity by the smaller one:

Vm/Vb = 35,000/1.423.93 = 24.58

Explanation:

The velocity of the meteorite is 24.58 times the velocity of the bowling ball.

A bird flies 3.7 meters in 46 seconds, what is its speed?

Answers

Answer:

Speed is 0.08 m/s.

Explanation:

Given the distance that the bird flies = 3.7 meters

The time is taken by the bird to fly the 3.7 meters = 46 seconds  

We have given distance and time. Now we have to find the speed at which the bird flies. So, to calculate the speed of the bird we have to divide the distance by the time.  

Below is the formula to find the speed.

Speed = Distance / Time

Now insert the given value in the formula.

Speed = 3.7 / 46 = 0.08 m/s

I am confused and need help

I am confused and need help

Answers

Answer: A
Explanation: we can eliminate options b & d right away because column 1 starts at 0 which indicates it’s the time column. Column 2 is showing some kind of speed or movement.. we have to decide if it’s velocity or acceleration.
Acceleration is defined as velocity/time
Velocity is displacement/time
Velocity is the correct chose because they are moving (displacing) over time

What is the momentum of a 8850 kg medium truck that is traveling with a velocity of 55 m/s west on the highway

Answers

Answer:

486,750 kg*m/s

Explanation:

Momentum is mass*velocity

M = m*v

M = 8850kg*55m/s

M = 486,750 kg*m/s

The momentum of an 8850 kg medium truck that is traveling with a velocity of 55 m/s west on the highway is 486750 kg m / s.

What is momentum?

Momentum is the result of a particle's mass and velocity. Being a vector quantity, momentum possesses both magnitude and direction. According to Isaac Newton's second equation of motion, the force acting on the particle equals the time rate of change of momentum.

According to Newton's second law, if a particle is subjected to a constant force for a specific amount of time, the result of the force and time (referred to as the impulse) is equal to the change in momentum.

Given:

The mass of the truck is, m = 8850 kg,

The velocity of the truck is, v = 55 m/s,

Calculate the momentum of the truck as shown below,

Momentum = m × v

Momentum = 8850 × 55

Momentum = 486750 kg m / s

Thus, the Momentum of the truck is 486750 kg m / s.

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1. At what displacement the kinetic energy and potential energy of a particle executing SHM will be equal when the amplitude is 3cm?​

Answers

The displacement at which the kinetic energy and potential energy of a particle executing SHM will be equal when the amplitude is 3cm is 1.5cm.

How does the amplitude of simple harmonic motion affect the ratio of kinetic to potential energy at a specific displacement?

The amplitude of simple harmonic motion affects the ratio of kinetic to potential energy at a specific displacement in the following way: as the amplitude increases, the ratio of kinetic to potential energy decreases. This is because the amplitude represents the maximum displacement from the equilibrium position, and as the amplitude increases, the potential energy of the particle increases, while the kinetic energy remains constant. Therefore, at a specific displacement, a particle with a larger amplitude will have a greater proportion of its energy in the form of potential energy, while a particle with a smaller amplitude will have a greater proportion of its energy in the form of kinetic energy.

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Look at the equation. What detail is missing? 3 m/s2= (33 m/s - X)/30 S

 Look at the equation. What detail is missing? 3 m/s2= (33 m/s - X)/30 S

Answers

Answer:

The starting velocity.

Explanation:

We must understand that this equation comes from the following equation of kinematics.

\(v_{f}=v_{o}+a*t\)

where:

Vf = final velocity = 33 [m/s]

Vo = starting velocity [m/s]

a = acceleration = 3 [m/s²]

t = time = 30 [s]

So, these values can be assembly in the following way:

\(v_{f}=v_{o}+a*t\\a*t=v_{f}-v_{o}\\3=\frac{33-v_{o}}{30}\)

Your telescope has an eyepiece of focal length 0.5 cm and can produce an image with magnification of 200. What is the focal length of your primary lens?

Answers

Answer:

Therefore, the focal length of the primary lens is 100 cm.

Explanation:

The formula for the magnification of a telescope is given by:

m = -f₁/f₂

where:

m = magnification

f₁ = focal length of the primary lens

f₂ = focal length of the eyepiece

Given that the magnification is 200 and the focal length of the eyepiece is 0.5 cm, we can rearrange the formula to solve for f₁:

m = -f₁/f₂

200 = -f₁/0.5

Multiplying both sides by 0.5:

100 = -f₁

Dividing both sides by -1:

f₁ = 100 cm

Therefore, the focal length of the primary lens is 100 cm.

Answer:

1m 0r 100 cm

Explanation:

The magnification of a telescope is given by the formula:

magnification = focal length of telescope / focal length of eyepiece

We are given the focal length of the eyepiece (0.5 cm) and the desired magnification (200). We can rearrange the formula to solve for the focal length of the telescope:

focal length of telescope = magnification x focal length of eyepiece

focal length of telescope = 200 x 0.5 cm = 100 cm = 1 m

Therefore, the focal length of the primary lens (or telescope) is 1 meter.

URGENT HELP PLS
(a) Find the frequency ratio between the two frequencies f1 = 320 Hz and
½2 = 576 Hz.
S) If we go down from / by an interval of a fourth, find the frequency ratio filfi.
(c) Find the frequency of f3.

Answers

The frequency of f3 is approximately 716 Hz.

What is frequency?

The frequency of a repeated event is its number of instances per unit of time. Hertz (Hz), which stands for the number of cycles per second, is a popular unit of measurement.

a. Given two frequencies, f1 and f2, the frequency ratio is as follows:

frequency ratio= \(\frac{f2}{f1}\)

Inputting the values provided yields:

frequency ratio = \(\frac{576}{320Hz}\) =1.8.

As a result, the difference in frequency between f1 = 320 Hz and f2 = 576 Hz is 1.8.

b. Since there are 12 half-steps in an octave and a fourth is a distance of 5 half-steps, going down a fourth requires dividing the frequency by \(2^{(4/12)}\). Hence, once a fourth is subtracted, the frequency ratio between f and f1 is:

frequency ratio= \(\frac{f}{ (f1 /f2 ) }\)=  \(\frac{f}{ (f1 / 1.3348) }\)

By dividing the numerator and denominator by 1.3348, we may make this more straightforward:

frequency ratio= (f × 1.33348)/f1

As a result, (f × 1.3348) / f1 is the frequency ratio between f and f1 after descending a fourth.

c. (c) To find the frequency of f3, we need to know the interval between f1 and f3. Let's assume that f3 is a fifth above f2. The frequency ratio for a fifth is given by: \(2^{(7/12)}\) = 1.49831

Therefore, the frequency of f3 is:

f3 = f1 × (\(2^{(7/12)}\)) × (\(2^{(7/12)}\)) = 320 Hz × 1.49831 ×1.49831 = 716 Hz

Therefore, the frequency of f3 is approximately 716 Hz.

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Please help with these questions

Please help with these questions

Answers

3) unit of the following are :

a) force = Newton

b) distance = meter

c) work = Joule

4) 90 J work has been done by her

5) 51 J work was done

6) He have done  \(10^{4}\) J  of work

7) no work is done

8) no work is done

9) 700 J is the work done on the car

10) 10.68 N  force is applied

3 ) unit of the following are :

a) force = Newton

b) distance = meter

c) work = Joule

4 ) work done = force * displacement

                       = 75 * 1.2 = 90 J

5 )  work done = force * displacement  

                        = 15 * 3.4 = 51 J

6 ) work done = force * displacement  

                        = 100 * 100 = \(10^{4}\) J

7) no work is done because no displacement occurred

8)  no work is done because no displacement took place

9) work done = force * displacement

                        = 12.5 * 56 = 700 J

10)  force = work done / displacement

                = 142 / 13.3 = 10.68 N

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A 1600 kg sedan goes through a wide intersection traveling from north to south when it is hit by a 2300 kg SUV traveling from east to west. The two cars become enmeshed due to the impact and slide as one thereafter. On-the-scene measurements show that the coefficient of kinetic friction between the tires of these cars and the pavement is 0.75, and the cars slide to a halt at a point 5.54 m west and 6.19 m south of the impact point. How fast was sedan traveling just before the collision? How fast was SUV traveling just before the collision?

Answers

Answer:

Explanation:

momentum of sedan of 1600 kg = 1600x v , where v is its velocity

momentum of suv of 2300 kg = 2300 x u where u is its velocity .

force of friction = ( 1600 + 2300 ) x 9.8 x  .75 ( fiction = μ mg )

= 28665 N

distance by which friction acted = √ (5.54² + 6.19²)

= 8.3 m

work done by friction

= 28665 x 8.3

= 237919.5 J

Total kinetic energy of cars = work done by friction

1/2 x 1600 x v² + 1/2 x 2300 u² = 237919.5

16 v² + 23 u² = 4758.4

1600 x v / 2300 u = 6.19 / 5.54

v / u = 1.6

v = 1.6 u

putting this equation in fist equation

40.96 u² + 23 u² = 4758.4

= 63.96 u² = 4758.4

u² = 74.4

u = 8.62 m /s

v = 13.8  m /s

A man is standing at a distance of 2m from a large plane mirror.
he walks 1m farther away from the mirror.how far is his image now from him​

Answers

Answer: 3m

Explanation: If he is already 2m away from the mirror then if he walks away 1m then it would equal out to 3. You could also add 1 to 2 so you could get the same results.

Josh starts his sled at the top of a 3.5-m high hill that has a constant slope of 25∘
. After reaching the bottom, he slides across a horizontal patch of snow. The hill is frictionless, but the coefficient of kinetic friction between his sled and the snow is 0.08.

Answers

If the coefficient of kinetic friction between Josh's sled and the snow is 0.08, he slides 6.97 meter from the base of the hill.

To find how far from the base of the hill Josh's sled ends up, we need to first find the speed of the sled at the bottom of the hill using the conservation of energy principle,

mgh = (1/2)mv², plugging in the values given in the problem, we get,

m(9.81 m/s²)(3.5 m) = (1/2)mv²

Simplifying and solving for v, we get,

v = √(2gh)

v = √(2(9.81 m/s²)(3.5 m))

v = 8.29 m/s

Now we can use the kinematic equation,

d = vt - (1/2)at, to find how far the sled slides on the horizontal patch of snow before coming to a stop, where d is the distance traveled, v is the initial velocity (8.29 m/s), a is the acceleration due to friction (-μg), and t is the time it takes to come to a stop (which we can find by setting v = 0 and solving for t),

0 = 8.29 m/s - μg*t

t = 8.29 m/s / μg

Substituting this value of t back into the kinematic equation, we get,

d = (8.29)(8.29/μg) - (1/2)μg(8.29/μg)²

d = 6.97 m

Therefore, Josh's sled ends up 6.97 meters from the base of the hill.

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