JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Kinematics

Two projectiles are thrown with same initial velocity making an angle of

4 5^{\circ}

and

3 0^{\circ}

with the horizontal respectively. The ratio of their respective ranges will be

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

Answer: (C)

Solution

The range of a projectile is given by

R = \frac{u ^{2} s i n ( 2 θ )}{g}

. For the first projectile at

4 5^{\circ}

R_{1} = \frac{u ^{2} s i n ( 9 0 ^{\circ} )}{g} = \frac{u ^{2}}{g}

. For the second at

3 0^{\circ}

R_{2} = \frac{u ^{2} s i n ( 6 0 ^{\circ} )}{g} = \frac{u ^{2} 3}{2 g}

. Therefore,

\frac{R _{1}}{R _{2}} = \frac{u ^{2} / g}{u ^{2} 3 / ( 2 g )} = \frac{2}{3}

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Single correct option

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