Question

A 50.0 kg woman, riding on a 10 kg cart, is moving east at 5.0 m/s. The woman  jumps off the front of the cart and lands on the ground at 7.0 m/s eastward. What is  the final velocity of the cart?

Answer 1

By Conservation Impulse Law:

$(m_1+m_2)v=m_1v_1+m_2v_2$

where $m_1$ is mass of cart, $m_2$ is mass of woman; $v$ is velocity of cart with woman before jumping, $v_1$ and $v_2$ are velocities of cart and woman after jumping.

$(50+10)\cdot5=50\cdot7-10v_1$

$v_1=\frac{50\cdot7-60\cdot5}{10}=5 m/s$ westward.