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` .

Explanation

A projectile will have same horizontal range for two angles of projection, ` theta and (90^(@)- theta).
Then horizontal range, ` R=(u^(2) sin 2 theta)/g`
` t_(t) =(2 u sin theta) g`
and ` t_(2) =(2 u sin (90^(@) -theta)/g =(2 u cos theta )/g `
:. t_(1) t_(2) =(2 u sin theta)/g xx (2 u cos theta)/g`
`= 2/g (u^(2) sin 2 theta )/g (2 g)/g`
Thus ` t_(1) t_(2) =2 R//g`