Question

A boy of mass 49.6 kg is initially on a skateboard of mass 2.00 kg, moving at a speed of 10.4 m/s. The boy falls off the skateboard, and his center of mass moves forward at a speed of 10.9 m/s. Find the final velocity of the skateboard.

Answer 1

Answer:2 m/s opposite to initial direction

Explanation:

Given

mass of boy $m=49.6 kg$

mass of skateboard $m_2=2 kg$

speed of skateboard $u=10.4 m/s$

speed of com of boy $v_0=10.9 m/s$

Let v be the speed of skateboard after fall

conserving momentum

$(m+m_2)u=m\times v_0+m_2\times v$

$(49.6+2)\cdot 10.4=49.6\times 10.9+2\times v$

$536.64=540.64+2v$

$2v=536.64-540.64$

$2v=-4$

$v=-2 m/s$

v=2 m/s opposite to original direction