Question

A railroad car is moving along a straight frictionless track. In each of the following cases, the car initially has a total mass (car and contents) of $200kg$ and is travelling with a velocity of $4m/s$. Find the final velocity of the car in each of the three cases.
(a) A $20kg$ mass is thrown sideways out of the car with a velocity of $2m/s$ relative to the car.
(b) A $20kg$ mass is thrown backward out of the car with a velocity of $4m/s$ relative to the car.
(c) A $20kg$ mass is thrown into the car with a velocity of $6m/s$ relative to the ground and opposite in direction to the velocity of the car.

Answer 1

There is no friction and car is moving on its track

By using the conservation of momentum we get

1).$200\times 4=200\times v_1$

$v_1=\frac{800}{200}$

$v_1=4m/s$

When a body is thrown sideways then there will not be any change in the velocity of the car.

2)$P=m_1{v}_1+m_2{v}_2$

$800=200\times v_1+20\times 2$

$v_1=3.8m/s$

As the body is thrown backward out of the car then the velocity of the car will be$3.8m/s$

3). $200\times 4=m_1{v}_1+m_2{v}_2$

$800=200\times v_1+20\times \left(-4\right)$

$v_1=4.4m/s$