JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Kinematics

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Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball.

T_{1}

and

T_{2}

are the total flying times of first and second ball, respectively, then the ratio of

T_{1}

and

T_{2}

is:

(A) $22 : 1$ ✓ Correct
(B) $2 : 1$
(C) $2 : 1$
(D) $4 : 1$

Answer: (A)

Solution

The maximum height

H = \frac{u ^{2} sin ^{2} θ}{2 g}

and the time of flight

T = \frac{2 u sin θ}{g}

use the same launch speed for both balls. From

H_{1} = 8 H_{2}

it follows that

sin^{2} θ_{1} = 8 sin^{2} θ_{2}

, so

sin θ_{1} = 22 sin θ_{2}

. Since the flight time is proportional to

sin θ

\frac{T _{1}}{T _{2}} = \frac{sin θ _{1}}{sin θ _{2}} = 22

. The ratio of the flight times is

22 : 1

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option

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