Question

A ball with a mass of `2 kg` is rolling at `5 m/s` and elastically collides with a resting ball with a mass of `9 kg`. What are the post-collision velocities of the balls?

Answer 1

`=>u=5/3ms^-1` and `v=20/27ms^-1`

Explanation:

If post collision velocities be u m/s for 1st one and v m/s for 2nd one ,then applying conservation of momentum
`uxx2+vxx9=2xx5+0xx9`
`=>uxx2+vxx9=10`
`=>vxx9=10-uxx2`
`=>vxx9=(5-u)xx2 .......(1)`

Now collision being elastic KE will be conserved and consequently the relative velocity of 1st object with respect to 2nd is reversed .
So `1/2xx2xx5^2+1/2xx9xx0^2=1/2xx2xxu^2+1/2xx9v^2`
`=>2xx5^2=2xxu^2+9v^2`
`=>2xx5^2-2xxu^2=9v^2`
`=>2xx(5^2-u^2)=9v^2`
`=>2xx(5+u)(5-u)=9v^2`
`=>(5+u)9v=9v^2`
`=>(5+u)=9v......(2)` `[:.v!=0]`
Comparing (1) and (2)
`5+u=10-2u`
`=>3u=10-5`
`=>u=5/3ms^-1`
and `v=20/27ms^-1`