A projectile can have same range `R` for two angles of projection. It `t_1 and t_2` are the times of flight in the two cases, then what is the product of two times of flight ?

Options

A. ` T_1 T_2 prop R`
B. ` T_1 T_2 prop R^2`
C. ` T_1 //T_2 = tan theta`
D. ` T_1 //T_2 = 1`

Answer

A, C

Explanation

Horizontal range is same when angle of projection is ` theta` and (90^@-theta)`
:. R = (u^2 sin 2 theta)/g = (2 u^2 sin cos theta)/g ` ….(1) ,brgt When angel of projection is ` theta`, then
` T_1 = (2 u sin (90^@ - theta))/g = ( 2 u cos theta)/g`
:. T_1T_2 = (4 u^2 sin theta cos theta)/g^2`
`= ((2 u^2 sin theta cos theta)/g) (2/g) = (2 R)/g`
T_1 T-2 prop R`
And ` T_1 /T_2 = (2 u sin theta//g)/(2 u cos theta//g) = tan theta`.