Question

a particle is projected at an angle 30 degree to the vertical with a speed of 20 m/s. find the instant when velocity is perpendicular to the initial direction of projection.
g = 10 m/s²

Answer 1

A particle is projected at angle 30° with vertical with and intial speed 20m/sec .
it means initial projection of particle inclines with horizontal (90-30)° = 60°

now,
U = 20°cos60°i + 20sin60°j
where U is initial velocity vector .

V = 20°cos60° i + ( 20°sin60° -gt) j
where V is final velocity vector .

A/Q U perpendicular upon V
hence , dot product of U and V = 0
e.g U.V = 0

( 20cos60°i + 20sin60°).{20cos60°i + (20sin60° -gt)j = 0

400cos²60° + 400sin²60° -20sin60°.gt = 0

400 - 20 × √3/2 × 10 t = 0

4 - √3t = 0

t = 4/√3 sec