Q 11-03-168JEE MainJEE Main 2019 (12 Apr, Shift 1)Medium
A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is:
Answer: (C) $\dfrac{2R}{g}$
The two angles are $\theta$ and $90^\circ - \theta$:
$$t_1t_2 = \frac{2u\sin\theta}{g}\cdot\frac{2u\cos\theta}{g} = \frac2g\cdot\frac{u^2\sin2\theta}{g} = \frac{2R}{g}$$
Solution by Sreeraj P, M.Sc Physics