A projectile is fired vertically upwards with a gun. At an altitude of 
, the projectile stops and explodes into two parts with masses 
and 
. The heavier part of the projectile continues to fly vertically upwards and the lighter part vertically downwards. The total energy at the time of the explosion is 
. Assume that the gravitational acceleration is 
and air resistance is ignored.
What is the speed at which each part of the projectile flies after the explosion, assuming that the potential energy on the ground is zero?
What is the velocity of each part of the projectile at time 
after the explosion?
