JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Kinematics

The ranges and heights for two projectiles projected with the same initial velocity at angles

4 2^{\circ}

and

4 8^{\circ}

with the horizontal are

R_{1}, R_{2}

and

H_{1}, H_{2}

respectively. Choose the correct option:

(A) $R_{1} < R_{2}$ and $H_{1} < H_{2}$
(B) $R_{1} > R_{2}$ and $H_{1} = H_{2}$
(C) $R_{1} = R_{2}$ and $H_{1} = H_{2}$
(D) $R_{1} = R_{2}$ and $H_{1} < H_{2}$ ✓ Correct

Answer: (D)

Solution

The range is

R = \frac{u ^{2} sin 2 θ}{g}

, so it depends on

sin 2 θ

. Here

2 θ

equals

8 4^{\circ}

and

9 6^{\circ}

, and

sin 9 6^{\circ} = sin (18 0^{\circ} - 9 6^{\circ}) = sin 8 4^{\circ}

, which gives

R_{1} = R_{2}

. The maximum height

H = \frac{u ^{2} sin ^{2} θ}{2 g}

grows with

θ

over this range, and since

4 8^{\circ} > 4 2^{\circ}

H_{2} > H_{1}

. The ranges are equal while

H_{1} < H_{2}

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Single correct option

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