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NEET Physics QUESTION #7327
Question 1

A body is projected at such an angle that the horizontal range is three times the maximum height. The angle of projection is:

  • $25°$
  • $33°$
  • $42°$
  • $53°$✔️
Correct Answer Explanation

Range: $R = \dfrac{u^2\sin2\theta}{g}$, Max height: $H = \dfrac{u^2\sin^2\theta}{2g}$

Given $R = 3H$: $\dfrac{\sin2\theta}{1} = 3\cdot\dfrac{\sin^2\theta}{2} \Rightarrow 2\sin\theta\cos\theta = \dfrac{3}{2}\sin^2\theta$

$\Rightarrow \tan\theta = \dfrac{4}{3} \Rightarrow \theta = \tan^{-1}\!\left(\dfrac{4}{3}\right) \approx \mathbf{53°}$