Question

A particle is projected from point O with velocity u in a direction making an angle $\alpha$ with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is

• A. u tanα
• B. u cotα
• C. u cosecα
• D. u secα

Answer 1

Answer: (B)

u cotα

Answer 2

Horizontal velocity at point $'O' = u\cos\alpha$

Horizontal velocity at point $'P' = v\sin\alpha$

In projectile motion horizontal component of velocity remains constant throughout the motion

∴ $v\sin\alpha = u\cos\alpha$ ⇒ $v = u\cot\alpha$