A shell is fired from a cannon with a velocity V at an angle `theta` with the horizontal direction. A the highest point i 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 priece immediately after the explocison is

Explanation

If .m. is mass of shell, at highest point, initial momentum
`= m(v cos theta)`, along horizontal
given, momentum of one fragment `=(m)/(3)(-v cos theta)`
momentum of second along horizontal = 0
If `.v_(1).` is speed of third fragment, from momentum conservation
`-(m)/(3)v cos theta +(m)/(3)v_(1)+0=m(v cos theta)`,
`v_(1)=4v cos theta`