
Let initial velocity of bullet be u.
Given, mass of bullet m=10g and mass of ball M=200g,
Initially ball is at height 5m and at rest, the only acceleration acting is due to gravity.
Time of flight of each ball and bullet is t=g2h.
Now, velocity of ball and bullet as v1=g2h30andv2=g2h120
As the collision is elastic, so applying conservation of linear momentum.
mu+M(0)=Mv1+mv2
⇒(0.01)u=(0.2)2h30g+(0.01)2h120g
⇒u=300+60=360ms−1