Two projectiles A and B are thrown with initial velocities of $40 \mathrm{~m} / \mathrm{s}$ and $60 \mathrm{~m} / \mathrm{s}$ at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Kinematics

Two projectiles A and B are thrown with initial velocities of

40 m / s

and

60 m / s

at angles

3 0^{\circ}

and

6 0^{\circ}

with the horizontal respectively. The ratio of their ranges respectively is

(g = 10 m / s^{2})

(A) $3 : 2$
(B) $2 : 3$
(C) $1 : 1$
(D) $4 : 9$ ✓ Correct

Answer: (D)

Solution

The range of a projectile is given by

R = \frac{u ^{2} s i n 2 θ}{g}

.

For projectile A:

R_{1} = \frac{( 40 ) ^{2} s i n ( 2 \times 30° )}{g} = \frac{1600 s i n 60°}{g} = \frac{1600 \times \frac{3}{2}}{g}

For projectile B:

R_{2} = \frac{( 60 ) ^{2} s i n ( 2 \times 60° )}{g} = \frac{3600 s i n 120°}{g} = \frac{3600 \times \frac{3}{2}}{g}

Ratio:

\frac{R _{1}}{R _{2}} = \frac{1600}{3600} = \frac{16}{36} = \frac{4}{9}

JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Single correct option

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