A shell is fired from a cannon with a velocity V at an angle θ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is

According to question the velocity initially is v and at an angle θ with horizontal. Hence horizontal component of the velocity is Vcosθ. Suppose, mass is M. hence, linear momentum is, MVcosθ.

Now, at highest point only horizontal velocity is present, hence, by conservation of momentum (as external force is not present),


(let’s assume it’s velocity to be x)


Solving this we get,

1