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MHT CET 2021 (23 Sep, Shift 2) · Centripetal Acceleration & Force

Centripetal Acceleration & Force question from MHT CET 2021 (23 Sep, Shift 2)

Q38MHT CET 2021 · 23 SEP · SHIFT 2Medium

Centripetal Acceleration & Force

A projectile is thrown with an initial velocity (ai^+bj^) m/s(a\hat{i} + b\hat{j})\text{ m/s}, where i^\hat{i} and j^\hat{j} are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is twice the maximum height reached by it, then

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Answer: (a)

  1. Here ux=au_x = a, uy=bu_y = b. Range R=2uxuyg=2abgR = \frac{2u_xu_y}{g} = \frac{2ab}{g}, maximum height H=uy22g=b22gH = \frac{u_y^2}{2g} = \frac{b^2}{2g}.
  2. R=2H⇒2abg=b2gR = 2H \Rightarrow \frac{2ab}{g} = \frac{b^2}{g}
  3. b=2ab = 2a
  4. So the answer is (a) b=2ab = 2a.
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