A shell is fired from a cannon with a velocity `v (m//sec.)` at an angle `theta` with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed (in `m//sec.`) of the other piece immediately after the explosion is

Explanation

At the highest point , the velocity is in horizontal direction and equal to `v cos theta`. One piece retraces its path, I.e. its velocity is `v cos theta` in opposite direction as shown . Let the velocity of other piece is `v'`.
Applying the momentum conservation at the higher point
`2 mv cos theta = - mv cos theta + mv'`
`v' = 3 v cos theta`