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A ball of mass m is thrown vertically upward. Another ball of mass 2m is thrown at an angle θ 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 1/x. The value of x is ______.

Asked in JEE Main 27th July 1st Shift 2022 · Maximum height

Answer: 1

Step-by-step solution

Same time in the air means the same vertical component of launch velocity: u₁ = u₂ cos θ.

Height depends only on that vertical component, H = (u_y²)/(2g), so the heights are equal: ratio 1 : 1, x = 1 (mass plays no part).

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