Question

A highly elastic rubber ball is tossed at a moveable wooden wall panel that is initially at rest. The ball’s initial velocity is 7.00 m/s to the right. After the elastic collision, the ball returns with a velocity of 4.90 m/s to the left, while the panel moves 2.09 m/s to the right. If the panel’s mass is 2.25 kg, what is the mass of the ball?

Answer 1

Given that the initial velocity of the ball is

$u_b=7\text{ m/s}$

towards right.

The final velocity of the ball is

$v_b=4.90\text{ m/s}$

towards the left.

The mass of the panel is M = 2.25 kg.

The initial velocity of the panel is

$u_p=\text{ m/s}$

The final velocity of the panel is

$v_p=\text{ 2.09 m/s}$

towards the right.

Let the mass of the ball be m.

According to the conservation of momentum

$mu_b+Mu_p=-mv_b+Mv_p$

Substituting the values, the mass of the ball will be

$\begin{gathered} m\times\text{ 7+2.25}\times0=-m\times4.90+2.25\times2.09 \\ 7m+4.90m=4.702\text{ } \\ m=0.395\text{ kg} \end{gathered}$

Thus, the mass of the ball is 0.395 kg.