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JEE Main 2025 (29 Jan, Shift 1) · Comparing Two Projectiles

Comparing Two Projectiles question from JEE Main 2025 (29 Jan, Shift 1)

Q7JEE Main 2025 · 29 JAN · SHIFT 1Easy

Comparing Two Projectiles

Two projectiles are fired with same initial speed from same point on ground at angles of (45∘−α)(45^\circ - \alpha) and (45∘+α)(45^\circ + \alpha), respectively, with the horizontal direction. The ratio of their maximum heights attained is:

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Answer: (d)

  1. H∝sin⁡2θH \propto \sin^2\theta, so H1H2=sin⁡2(45∘−α)sin⁡2(45∘+α)\frac{H_1}{H_2} = \frac{\sin^2(45^\circ - \alpha)}{\sin^2(45^\circ + \alpha)}
  2. sin⁡2(45∘∓α)=1−cos⁡(90∘∓2α)2=1∓sin⁡2α2\sin^2(45^\circ \mp \alpha) = \frac{1 - \cos(90^\circ \mp 2\alpha)}{2} = \frac{1 \mp \sin 2\alpha}{2}
  3. H1H2=1−sin⁡2α1+sin⁡2α\frac{H_1}{H_2} = \frac{1 - \sin 2\alpha}{1 + \sin 2\alpha}
  4. So the answer is (d).
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