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Question

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

A
u cosθ
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B
u tanθ
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C
u cotθ
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D
u secθ
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Solution

## The correct option is A u cotθSince the new velocity is perpendicular to the initial velocity and the initial velocity makes an angle θ with the horizontal, this new velocity must make an angle 90∘−θ with the horizontal.Throughout the motion, only external force acting is gravitational in the vertical direction. Thus the horizontal velocity remains the same.Thus ucosθ=vsinθ⟹v=ucotθ

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