Question

Ball A (7kg) and ball B (3kg) hit each other in a perfectly elastic collision. If ball A has an initial velocity of 12 m/s and ball B has an initial velocity of -1 m/s. What are the final velocities of each ball?

Answer 1

Explanation:

Mass of ball A, $m_A=7\ kg$

Mass of ball B, $m_B=3\ kg$

Initial velocity of ball A, $u_A=12\ m/s$

Initial velocity of ball B, $u_B=-1\ m/s$

We need to find the final velocity of each ball. For a perfectly elastic collision, the coefficient of restitution is equal to 1. It is given by :

$e=\dfrac{v_B-v_A}{u_A-u_B}$

$v_A\ and\ v_B$ are final velocities of ball A and B

$1=\dfrac{v_B-v_A}{13}$

$v_B-v_A=13$...........(1)

Using the conservation of linear momentum as :

$m_Au_A+m_Bu_B=m_Av_A+m_Bu_B$

$7(12)+3(-1)=7v_A+3u_B$

$7v_A+3u_B=81$..............(2)

On solving equation (1) and (2) using calculator we get :

$v_A=4.2\ m/s$

$v_B=17.2\ m/s$

So, the final velocities of ball A and B are 4.2 m/s and 17.2 m/s. Hence, this is the required solution.