Solution -
Initial momentum = final momentum
mv = ( M + m )Vf
Vf = mv / ( M + m )
Now we got the final velocity of the Block + bullet system now this system will move with Vf and then it reaches to some height (H) till whole of it's kinetic energy is converted into potential energy .
Applying the energy conservation principle = >
(1/2) x ( M + m ) x Vf2 = ( M + m ) x g x H
H = (1/2g) x Vf2
H = (1/2g) x [mv / ( M + m ) ]2
H / V2 = m2 / [2g( M + m )2]
This is the required relation between the initial velocity and the height .
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