A shell of mass 2 kg moving at a rate of 4 m//s suddenly explodes into two equal fragments. The fragments go in directions inclined with the original line of motion with equal velocities, If the explosion imparts 48 J of translational kinetic energy to the fragments, find the velocity and direction of each fragment.

A shell of mass 2 kg moving at a rate of 4 m//s suddenly explodes into

1.	A shell of mass 2 kg moving at a rate of 4 m//s suddenly explodes into two equal fragments. The fragments go in directions inclined with the original line of motion with equal velocities, If the explosion imparts 48 J of translational kinetic energy to the fragments, find the velocity and direction of each fragment.
Answer» Solution :Conservation of linear momentum of along `X` and `Y` axes gives `"mu"=m_(1)v_(1) costheta_(1)+m_(2)v_(2)costheta_(2)` i.e. `2u=1xxv_(1)costheta_(1)+1xxv_(2)costheta_(2)` `implies v_(1)costheta_(1)+v_(2)costheta_(2)=2u`…………i and `0=m_(1)v_(2)sintheta+m_(2)v_(2)sintheta_(2)` As `m_(1)=m_(2)=1KG` `implies v_(1)sintheta_(1)=v_(2)sintheta_(2)` As `v_(1)=v_(2)=v`(say) `implies theta_(1)=theta_(2)=theta` (say) from eqn i `implies v costheta+vcostheta=2u` `implies v costheta =u=4`...............II Also conservation of ENERGY gives `1/2mu^(2)+48=1/2(m_(1))v^(2)+1/2(m_(2))v^(2)` `implies 1/2xx2xx(4)^(2)+48=1/2xx1v^(2)+1/2xx1v^(2)` or `v^(2)=64` `implies v=8m//s` `costheta=u/v=4/8=1/2` `implies theta=60^(@)`