Two projectiles P1 and P2 thrown with speed in the ratio √(3): √(2), attain the same height during their motion. If P2 is thrown at an angle of 60 ° with the horizontal, the angle of projection of P1 with horizontal will be: (a) 15 ° (b) 30 ° (c) 45 ° (d) 60 °

Answer: (c). Same maximum height means equal vertical components: u₁sin θ₁ = u₂sin 60°. sin θ₁ = (√(2))/(√(3))·√(3)/2 = 1/√(2) So θ₁ = 45°, answer (c).

Two projectiles P1 and P2 thrown with speed in the ratio √(3): √(2)… | JEE Main 2022 (30 Jun, Shift 1)

Q19JEE Main 2022 · 30 JUN · SHIFT 1Medium

Comparing Two Projectiles

Two projectiles P1 and P2 thrown with speed in the ratio $\sqrt{3}$ : $\sqrt{2}$ , attain the same height during their motion. If P2 is thrown at an angle of 60 $^\circ$ with the horizontal, the angle of projection of P1 with horizontal will be:

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Answer: (c)

Same maximum height means equal vertical components: $u_1\sin\theta_1 = u_2\sin 60^\circ$ .
$\sin\theta_1 = \frac{\sqrt{2}}{\sqrt{3}}\cdot\frac{\sqrt{3}}{2} = \frac{1}{\sqrt{2}}$
So $\theta_1 = 45^\circ$ , answer (c).

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