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

Step-by-step 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=(v_B-v_A)/(u_A-u_B)`

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

`1=(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.