Q 11-03-044JEE MainJEE Main 2026 (8 Apr, Shift 2)Easy
Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $R$. If the time of flight of these bodies are $5$ s and $10$ s, respectively, then the value of $R$ is ______ m. (Take $g = 10\ \text{m/s}^2$)
Answer: (A) $250$
Equal ranges at the same speed mean the angles are $\theta$ and $90^\circ - \theta$.
$T_1 = \dfrac{2u\sin\theta}{g}$, $T_2 = \dfrac{2u\cos\theta}{g}$, so
$$T_1T_2 = \frac{4u^2\sin\theta\cos\theta}{g^2} = \frac{2}{g}\cdot\frac{u^2\sin 2\theta}{g} = \frac{2R}{g}$$
$R = \dfrac{gT_1T_2}{2} = \dfrac{10 \times 5 \times 10}{2} = 250$ m.
Solution by Sreeraj P, M.Sc Physics