Hello,

Given that the shell is moving horizontally and explodes in two equal pieces. One particle is moving upward with a momentum 4p and the momentum at time of explosion is 3p.

Kinetic Energy = ?

By using law of conservation of momentum,

Total Momentum of particle before explosion = Total Momentum of particle after explosion

So, 3P ( i )= 4P ( j )  + P2

So, Magnitude of P2 = 5P

So, gain in Kinetic Energy

= ( 16 P^2 / m ) + ( 25 P^2 / m ) - ( 9 P^2 / 2m )

= 73 P^2 / 2m

Best Wishes.