Question

A 0.060 ???????? tennis ball, moving with a speed of 5.28 m/???? , has a head-on collision with a 0.080 ???????? ball initially moving in the same direction at a speed of 3.00 m/ ???? . Assume that the collision is perfectly elastic. Determine the velocity (speed and direction) of both the balls after the collision.

Answer 1

Explanation:

It is given that,

Mass of the tennis ball, $m_1=0.06\ kg$

Initial speed of tennis ball, $u_1=5.28\ m/s$

Mass of ball, $m_2=0.08\ kg$

Initial speed of ball, $u_2=3\ m/s$

In case of elastic collision, the momentum remains conserved. The momentum equation is given by :

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$v_1\ and\ v_2$ are final speed of tennis ball and the ball respectively.

$0.06\times 5.28+0.08\times 3=0.06v_1+0.08v_2$

$0.06v_1+0.08v_2=0.5568$..............(1)

We know that the coefficient of restitution is equal to 1. It is given by :

$\dfrac{v_2-v_1}{u_1-u_2}=1$

$\dfrac{v_2-v_1}{5.28-3}=1$

${v_2-v_1}=2.28$.................(2)

On solving equation (1) and (2) to find the values of velocities after collision.

$v_1=5.28\ m/s$

$v_2=3\ m/s$

So, the speed of both balls are 5.28 m/s and 3 m/s respectively. Hence, this is the required solution.