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Question

A particle is projected from a point O with a velocity u in a direction making an angle α upward with the horizontal. After some time at point P it is moving at right angle with its initial direction of projection. The time of flight from O to P is


A

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B

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C

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D

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Solution

The correct option is B


When body projected with initial velocity u by making angle α with the horizontal. Then after time t, (at point P) it’s direction is perpendicular to u

Magnitude of velocity at point P is given by v = u cot α (from sample problem no. 9)

For vertical motion : Initial velocity (at point O) =u sin α

Final velocity (at point P) =v cos α=u cot α cos α

Time of flight (from point O to P) = t

Applying first equation of motion v=ugt

u cot α cos α=u sin αgt t=u sin α+u cot α cos αg=ug sin α[sin2 α+cos2 α]=u cosec αg


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