Question

What is the mass of the skateboard? A 47.4 kg students runs down the sideral and jumps with a horizontal speed of 4.2 m/s onto a stationary skateboard. The student and skateboard move down the side walk with a speed of 3.95 m/s.

Answer 1

Let's apply the law of conservation of linear momentum:

$$m_1v_1=(m_1+m_2)v_c,$$ $$m_2=\dfrac{m_1(v_1-v_c)}{v_c},$$ $$m_2=\dfrac{47.4\ kg\cdot(4.2\ \dfrac{m}{s}-3.95\ \dfrac{m}{s})}{3.95\ \dfrac{m}{s}}=3\ kg.$$