A shell is fired vertically upwards with a velocity `v_(1)` from the deck of a ship travelling at a speed of `v_(2)`. A person on the shore observes the motion of the shell as parabola. Its horizontal range is given by:-

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)`