Two particles are projected from the same point with the same speed at different angles `theta_1` & `theta_2` to the horizontal. They have the same range. Their times of flight are `t_1` & `t_2` respectfully

Options

A. `theta_1+theta_2=90^@`
B. `t_1/t_2=tantheta_1`
C. `t_1/t_2=tantheta_2`
D. `t_1/(sintheta_1)=t_2/(sintheta_2)`

Answer

A, B, D

Explanation

`(u^(2) sin 2theta_(1))/(g)=(u^(2) sin 2theta_(2))/(g) rArr sin 2theta_(1)=sin (180-2theta_(2)) rArr theta_(1)+theta_(2)=90^(2)`
`t_(1)=(2u sin theta_(1))/(g) and t_(2)=(2u sin theta_(2))/(g) rArr (t_(1))/(sin theta_(1))=(t_(2))/(sin theta_(2))=(2u)/(g)`
`t_(1)//t_(2)=(sin theta_(1))/(sin theta_(2))=(sin theta_(1))/(cos theta_(1))=tan theta_(1)=cot theta_(2)`