JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Kinematics

The two projectiles are projected with the same initial velocities at the

1 5^{\circ}

and

3 0^{\circ}

with respect to the horizontal. The ratio of their ranges is

1 : x

. The value of

x

(A) $2$
(B) $3$ ✓ Correct
(C) $23$
(D) $\frac{1}{2}$

Answer: (B)

Solution

The horizontal range is

R = \frac{u ^{2} sin 2 θ}{g}

. For

θ = 1 5^{\circ}

R_{1} = \frac{u ^{2} sin 3 0 ^{\circ}}{g}

, and for

θ = 3 0^{\circ}

R_{2} = \frac{u ^{2} sin 6 0 ^{\circ}}{g}

. The ratio is

\frac{R _{1}}{R _{2}} = \frac{sin 3 0 ^{\circ}}{sin 6 0 ^{\circ}} = \frac{1/2}{3 /2} = \frac{1}{3}

. Written as

1 : x

this gives

x = 3

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Single correct option

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