A cannon of mass `5m` (including a shell of mass m) is at rest on a smooth horizontal ground, fires the shell with its barrel at an angle `theta` with the horizontal at a velocity u relative to cannon. Find the horizontal distance of the point where shell strikes the ground from the initial position of the cannon :-

Options

A. `(4u^(2) sin 2theta)/(5g)`
B. `(u^(2) sin 2theta)/(5g)`
C. `(3u^(2) sin 2theta)/(5g)`
D. `(8u^(2) sin 2theta)/(5g)`

Answer

A

Explanation

COLM :
Along horizontal

`0 = m(u cos theta - v) -4 mv rArr v = (u cos theta)/(5)`
`:.` velocity of shell along horizontal w.r.t ground
`= u cos theta - (u cos theta)/(5) = (4)/(5) (u cos theta)`
Time. of flight `T = (2u sin theta)/(g)`
`:, x =` horizontal displacement
`= ((4)/(5)u cos theta) ((2u sin theta)/(g)) = (4u^(2) sin 2theta)/(5g)`