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## Homework Statement

A stationary car with 4 people in it has mass 100 kg. The mass of each of the person is 75 kg. They jump off the car with speed 2 ms

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__relative to the car__. Calculate the speed of the car if

a. 4 people jump at once

b. They jump one by one each time

## Homework Equations

momentum and kinematics maybe

## The Attempt at a Solution

1 = people

2 = car

a) m

_{1}u

_{1}+m

_{2}u

_{2}= m

_{1}v

_{1}+m

_{2}v

_{2}

0 = 4 x 75 x 2 - 100 x v

_{2}

v

_{2}= 6 ms

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b) 1st person jumps

0 = 75 x 2 - 325 x v2

v2 = 6/13 ms

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2nd person jumps

the speed of 2nd person relative to the car = 2 + 6/13 = 32/13 ms

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m1 u1 + m2 u2 = m1 v1 + m2 v2

0 - 325 x 6/13 = 75 x 32/13 - 250 x v2

v2 = 87/65 ms

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3rd person jumps

the speed of 3rd person relative to the car = 2 + 87/65 = 217/65 ms

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m1 u1 + m2 u2 = m1 v1 + m2 v2

0 - 250 x 87/65 = 75 x 217/65 - 175 x v2

v2 = 117/35 ms

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4th person jumps

the speed of 4th person relative to the car = 2 + 117/35 = 187/35 ms

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m1 u1 + m2 u2 = m1 v1 + m2 v2

0 - 175 x 117/35 = 75 x 187/35 - 100 x v2

v2 = 69/7 ms

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the final speed of the car is 69/7 ms

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I am not sure whether my answers are correct. Can someone please help checking my answers? Thank you very much