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A projectile can have the same range R for two angles of projection. If $t_{1}$ and $t_{2}$ be the times of flight in two cases, then what is the product of two times of flight?
Explanation
$t_{1} = 2u \sin \theta/g$ and $t_{2} = 2u \sin(90 - \theta)/g = 2u \cos \theta/g$ $\therefore t_{1}t_{2} = 4u^{2}\cos \theta \sin \theta/g^{2} = \frac{2}{g} [u^{2}\sin 2\theta/g] = (2/g)R$, where R is the range. Hence $t_{1}t_{2} \propto R$