A projectile can have the same range` R` for two angle of projection . If ` t-1` and ` t_2` be the terms of flight in the two cased then the initial velocity of projectile is?

Options

A. `1/4 gt t_1 t_2`
B. `1/2 gt t_1 t_2`
C. ` 1/2 gt (t_1 +t_2)^2`
D. `1/2 gt (t_1^2 +t_2^2)^(1/2)`

Answer

D

Explanation

Horizontal range is same whe angle fo projection is ` alpha ` or ` (90^2- alpha)` . ltBrgt :. R= (u^2 sin 2 alpha)/g , ` t_1 = ( 2 u sin alpha)/g …(i)
and ` t_2 = (2 u sin ( 90^@ -alpha))/g = ( 2 u cos alpha)/g ` …(ii) `
From (i), ` isn alpha = gt_1//2 u,`
From (ii) , cos alpha = gt _2//2 u`
:. sin ^2 alpha + cos^2 alpha= ( g/(2u)) ^2 (t_1^1 _t_1^2)`
or ` u = g/2 (t_1^2 +t_1^2) ^(1//2)`.