Q 11-03-121JEE MainJEE Main 2022 (27 Jul, Shift 1)Easy
A ball of mass $m$ is thrown vertically upward. Another ball of mass $2m$ is thrown at an angle $\theta$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\dfrac1x$. The value of $x$ is ______ .
Numerical value type. Enter your answer.
Answer: 1
Time of flight $T = \dfrac{2u_y}{g}$ depends only on the vertical component of velocity. Equal times mean equal $u_y$.
Maximum height $H = \dfrac{u_y^2}{2g}$ also depends only on $u_y$, so the heights are equal: ratio $1 = \dfrac11$, $x = 1$.
Solution by Sreeraj P, M.Sc Physics