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Question

A body is projected at time t = 0 with a velocity u at an angle θ with the horizontal. The horizontal and vertical components of its velocity will become equal at a time t (t0) if,



A

If 0 θ π4

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B

If π4 θ  π2

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C

If 0   θ  π6

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D

for no value of θ

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Solution

The correct option is C

If π4 θ  π2


Horizontal component of velocity at a time t is vx=u cos θ

Vertical component of velocity at that time t is vy=u sin θgt

They will become equal at time t if ucos θ=u sin θgt

Which gives t=u(sin θcos θ)g

Now t must be positive. Hence sin θ>cos θ or θ > π/4.


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