A projectille can have the same range` R` for two angles of projection. If ` t_(1)` and `t_(2)` be the time of flight in the two cases, then find the relation between ` t_(1), t_(2)` and `R` .

Options

A. `t_(1)t_(2)=R_(2)`
B. `t_(1)t_(2)=(1)/(R^(2))`
C. `t_(1)t_(2)=R`
D. `t_(1)t_(2)=(1)/(R)`

Answer

c

Explanation

`t_(1)=(2u sin theta)/(g)`
`t_(2)=(2u sin(90^(@)-theta))/(g)=(2ucos theta)/(g)`
`t_(1)t_(2)=(2u sin theta)/(g)xx(2ucos theta)/(g)`
`=(2)/(g)((u^(2))/(g)sin 2 theta)=(2R)/(g)`
`therefore t_(1)t_(2)propR`