A ball is thrown from the ground so as to just clear a wall `10 m` high at a distance of `20 m` and falls at a distance of `40 m` from the wall. The magnitude and direction of the projection velocity is

Options

A. `10 m//s, 30^(@)`
B. `25 m//s, 60^(@)`
C. `25 m//s, tan^(-1) (3//4)`
D. `10 m//s, tan^(-1) (3//4)`

Answer

C

Explanation

For the point `P, x = 20, y = 10`
`R = 60 m`
`y = x tan theta (1 - (x)/(R ))`
`10 = 20 tan theta(1 - (20)/(60)) = (40)/(3) tan theta`
`tan theta = 3//4 rArr theta = tan^(-1) (3//4)`

`sin theta = 3//5, cos theta = 4//5`
`R = (u^(2))/(g) 2 sin theta cos theta rArr 60 = (u^(2))/(10) xx 2 xx (3)/(5) xx (4)/(5)`
`u^(2) = 625 rArr u = 25 m//s`