Q 11-03-076JEE MainJEE Main 2024 (30 Jan, Shift 2)Medium
Projectiles $A$ and $B$ are thrown at angles of $45^\circ$ and $60^\circ$ with the vertical respectively from the top of a $400\ \text{m}$ high tower. If their times of flight are the same, the ratio of their speeds of projection $v_A : v_B$ is:
Answer: (D) $1:\sqrt2$
The time of flight from the tower depends only on the vertical component of velocity (both fall the same 400 m). Equal times need equal vertical components:
$$v_A\cos45^\circ = v_B\cos60^\circ \Rightarrow \frac{v_A}{v_B} = \frac{1/2}{1/\sqrt2} = \frac1{\sqrt2}$$
Solution by Sreeraj P, M.Sc Physics