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JEE Main 2019 (12 Apr, Shift 1) · Comparing Two Projectiles

Comparing Two Projectiles question from JEE Main 2019 (12 Apr, Shift 1)

Q25JEE Main 2019 · 12 APR · SHIFT 1Medium

Comparing Two Projectiles

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is -

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Answer: (a)

  1. The two ways are angles θ\theta and 90∘−θ90^\circ - \theta: t1=2usin⁡θgt_1 = \frac{2u\sin\theta}{g}, t2=2ucos⁡θgt_2 = \frac{2u\cos\theta}{g}
  2. t1t2=2g⋅2u2sin⁡θcos⁡θg=2Rgt_1 t_2 = \frac{2}{g}\cdot\frac{2u^2\sin\theta\cos\theta}{g} = \frac{2R}{g}
  3. So the answer is (a) 2Rg\frac{2R}{g}.
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