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

Options

A. `3 upsilon cos theta`
B. `2 upsilon cos theta`
C. `(3//2) upsilon theta`
D. `(sqrt(3)//2) upsilon cos theta`

Explanation

Let `m` be the mass of the shell. Total momentum at the highest point before explosion`m upsilon cos theta`
One of the pieces of mass `m//2` will retrace its path to the cannon only when its veocity is `(- upsilon cos theta)`. Therefor, its momentum`=-(m)/(2) upsilon cos theta `. Applying principle of conservation of linear momentum
`(m)/(2) upsilon^(')-(m)/(2) upsilon cos theta=m upsilon cos theta`
`(m)/(2) upsilon^(')=(3)/(2) m upsilon cos theta`
`:. upsilon^(')= 3 upsilon cos theta`