Question

Two particle are projected from the same point with same speed in same vertical plane but at different angles of projection such that they produce the same range. If the ratio of their times of flight is $\sqrt{3} : 1$ , their angles of projection are

Moderate

Solution

It angle of projection of one particle is $α$ , that of the other particle must be $(90^{o} - α)$
$∴ T_{α} = \frac{2 u \sin α}{g} and T_{β} = \frac{2 u \sin (90^{o} - α)}{g} = \frac{2 u \cos α}{g}$
Now $\frac{T_{α}}{T_{β}} = \sqrt{3} \Rightarrow \tan α = \sqrt{3} \Rightarrow α = 60^{o}$

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