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JEE Main 2022 (27 Jul, Shift 1) · Comparing Two Projectiles

Comparing Two Projectiles question from JEE Main 2022 (27 Jul, Shift 1)

Q20JEE Main 2022 · 27 JUL · SHIFT 1Medium

Comparing Two Projectiles

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 $\frac{1}{x}$ . The value of x is _____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 1

Time of flight $T = \frac{2u_y}{g}$ depends only on the vertical component $u_y$ (not on mass).
Same $T$ means same $u_y$ , so same height $H = \frac{u_y^2}{2g}$ .
Ratio $\frac{1}{x} = 1 \Rightarrow x = 1$

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