A ball is projected towards right from point A at an angle `theta` with vertical. A system imparts an acceleration `g tan theta` to the ball towards left along negative x-axis. The ball will return to ground at :

Options

A. A
B. B left to point A
C. C right to point A
D. None of the above

Answer

A

Explanation

`T = (2 u sin(90^(@) - theta))/(g) = (2u cos theta)/(g)`
`s_(n) = u_(x) T + (1)/(2) a_(x) T^(2)`
`=u sin theta x (2u cos theta)/(g) + (1)/(2) (-g tan theta) ((2u cos theta)/(g))^(2)`
`= (u^(2) sin theta)/(g) - (1)/(2) g. (sin theta)/(cos theta) xx (4u^(2) cos^(2) theta)/(g^(2))`
`= (u^(2) sin 2 theta)/(g) - (u^(2) sin 2 theta)/(g)`
Hence particle returnes to A.