A particle is projected at an angle with horizontal. If `T` is the time of flight and `R` is a horizontal range, then `theta` is

Options

A. `cot^(-1)((g T^(2))/(R ))`
B. `cot^(-1)((g T^(2))/(2 R ))`
C. `tan^(-1)((2R )/(g T^(2)))`
D. `tan^(-1)((g T^(2))/(2 R))`

Answer

D

Explanation

`T = (2 u sin theta)/(g), R = (u^(2))/(g).2 sin theta cos theta`
`(T^(2))/(R ) = (4 u^(2) sin^(2) theta//g^(2))/(2u^(2) sin theta cos theta//g) = (2 tan theta)/(g)`
`tan theta = (g T^(2))/(2 R) rArr theta = tan^(-1)((g T^(2))/(2 R))`