A shell is fired from a cannon with a velocity 'v' at an angle $ '\theta'$ with the horizontal. At the highest point in its path it explodes into two pieces of equal masses. One of the pieces retraces its path and reaches the cannon. Then the velocity of the other piece immediately after collision is :

Question

$\begin {array} {1 1} (1)\;2\: v\: \cos\:\theta & \quad (2)\;\large\frac{3}{2}\: v\: \cos\:\theta \\ (3)\;3\: v\: \cos\:\theta & \quad (4)\;v\: \cos\:\theta \end {array}$