At the highest point only horizontal component of velocity exists.
Let x be the peak point
Apply conservation of momentum principle we have
Momentum before explosion is equal to momentum after explosion
therefore, mV cos &θ = momentum before explosion
= momentum after explosion
= Velocity of second piece
After explosion half of mass traces back the path and hits the cannon, so its velocity will be equal to V cos &θ but in opposite direction.
therefore, From momentum conservation
mV cos &θ =
= 3 V cos &θ