First slide

Projectile motion

Question

A particle is projected from point O with velocity u in a direction making an angle $α$ 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

Moderate

A

$u \tan α$
B

$u \cot α$
C

$u cosec α$
D

$u \sec α$

Solution

Horizontal velocity at point $^{'} O^{'} = u \cos α$
Horizontal velocity at Point $^{'} P^{'} = v \sin α$
In projectile motion horizontal component of velocity remains constant throughout the motion
$\begin{array}{l} ∴ v \sin α = u \cos α \\ \Rightarrow v = u \cot α \end{array}$

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