Question

A particle is projected with a velocity $u$ making an angel $\theta$ with the horizontal. At any instant its velocity becomes $v$ which is perpendicular to the initial velocity $u$. Then $v$ is

• A. $u\cos \theta$
• B. $u\sec \theta$
• C. $u\cot \theta$
• D. $u\tan \theta$

Answer 1

The correct option is C $u\cot \theta$

1. Draw a diagram of given problem.

2. Find $v$

Throughtout the motion, only external force acting is gravitational in the vertical direction. Hence, the original velocity remains same. Therefore,

$v\sin \theta =u\cos \theta$

$v=u\cot \theta$

Final answer :(d)