First slide

Projectile motion

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

Difficult

A

$\frac{u \sin α}{g}$
B

$\frac{u cosec α}{g}$
C

$\frac{u \tan α}{g}$
D

$\frac{u \sec α}{g}$

Solution

when the body projected with initial velocity $\vec{u}$ by making angle a with the horizontal, then after time t, (at point P) its direction is perpendicular to $\vec{u}$ . Magnitude of velocity at point P is given by $v = u \cot α$
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= u - gt
$\begin{array}{l} t - u \cot α \cos α = u \sin α - g t \\ ∴ t = \frac{u \sin α + \cot α \cos α}{g} \\ = \frac{u}{g \sin α} [\sin^{2} α + \cos^{2} α] = \frac{u cosec α}{g} \end{array}$

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