Question

A projectile at any instant during its flight has velocity $5m/s$ at ${30}^o$ above the horizontal. How long after this instant, will it be moving at right angle to the given direction?

Answer 1

Given,

Projectile upward velocity$v_y=V\sin \theta =5\sin {30}^o=2.5m/s$

Normal velocity is at angle $-({90}^o-{30}^o)=-{60}^o$

Projectile downward velocity$v{{}^{\prime }}_y=V\sin (-{60}^o)=-5\cos {30}^o=-2.5\sqrt{3}m/s$

Apply first equation of motion

$v{{}^{\prime }}_y=v_y+at$

$-2.5\sqrt{3}=2.5-gt$

$t=\frac{-2.5\sqrt{3}-2.5}{-10}=0.68\sec$

After $0.68\sec$both velocities become normal.