A projectile can have the same range R for two angles of projection. If `t_(1)` and `t_(2)` be the times of flight in the two cases:-

Options

A. `t _ 1 t _ 2 prop R ^ 2 `
B. ` t _ 1 t _ 2 prop R `
C. `t _ 1 t _ 2 prop (1)/(R ) `
D. ` t _ 1 t _ 2 prop (1)/(R^2 ) `

Answer

B

Explanation

For same range, angles of projection should be `theta and (90^(@)-theta)` So, time of flights. `t_(1)=(2u sin theta)/(g) and t_(2)=(2u sin (90^(@)-theta))/(g)=(2u cos theta)/(g)`
`t_(1)t_(2)=(4u^(2)sin theta cos theta)/(g^(2)) rArr t_(1)t_(2)=2/g ((u^(2) sin 2 theta))/(g)=(2R)/(g) rArr t_(1)t_(2) alpha R`