A particle is projected with velocity u at angle `theta` with horizontal. Find the time when velocity vector is perpendicular to initial velocity vector.

Options

A. `u//g sin theta`
B. `u//g cos theta`
C. `2u//g sin theta`
D. `2u tan theta`

Answer

A

Explanation

Since, `v _|_ u` or `v.u = 0`
or `(u +a t) u = 0`
or `u. u +(a.u) t = 0`
or `u^(2) + gut cos (90^(@) + theta) = 0`
(angle between u and u is `90^(@) + theta)`
or `u - g t sin theta = 0` or `t = (u)/(g sin theta)`