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?

1 Answer
P dilip_k
Mar 12, 2016

=>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

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