Q 11-03-169JEE MainJEE Main 2019 (12 Apr, Shift 2)Medium
Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct?
Answer: (D) $R^2 = 16h_1h_2$
Equal ranges need angles $\theta$ and $90^\circ - \theta$:
$$h_1h_2 = \frac{u^2\sin^2\theta}{2g}\cdot\frac{u^2\cos^2\theta}{2g} = \frac{1}{16}\left(\frac{u^2\cdot2\sin\theta\cos\theta}{g}\right)^2 = \frac{R^2}{16}$$
$$R^2 = 16h_1h_2$$
Solution by Sreeraj P, M.Sc Physics