Question

A particle is projected with a velocity $u$ making anangle $\theta$ with the horizontal. At any instant, its velocity $v$ is at right angles to its initial velocity $u$; then $v$ is:

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

Answer 1

Answer: (C)

$u$ $cot\theta$

Since the new velocity is perpendicular to the initial velocity and the initial velocity makes an angle $\theta$ with the horizontal, this new velocity must make an angle ${90}^{\circ }-\theta$ with the horizontal.

Throughout the motion, only external force acting is gravitational in the vertical direction. Thus the horizontal velocity remains the same.

Thus $ucos\theta =vsin\theta$

$⟹v=ucot\theta$