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JEE Main 2019 (12 Apr, Shift 2) · Comparing Two Projectiles

Comparing Two Projectiles question from JEE Main 2019 (12 Apr, Shift 2)

Q24JEE Main 2019 · 12 APR · SHIFT 2Medium

Comparing Two Projectiles

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1 and h2. Which of the following is correct?

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Answer: (b)

  1. Same range: angles θ\theta and 90∘−θ90^\circ - \theta, so h1=u2sin⁡2θ2gh_1 = \frac{u^2\sin^2\theta}{2g}, h2=u2cos⁡2θ2gh_2 = \frac{u^2\cos^2\theta}{2g}
  2. h1h2=u4sin⁡2θcos⁡2θ4g2h_1 h_2 = \frac{u^4\sin^2\theta\cos^2\theta}{4g^2}, while R2=4u4sin⁡2θcos⁡2θg2R^2 = \frac{4u^4\sin^2\theta\cos^2\theta}{g^2}
  3. R2=16h1h2R^2 = 16h_1 h_2
  4. So the answer is (b).
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