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
Mar 12, 2016

Answer:

#=>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#