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NEET Physics QUESTION #7328
Question 1

A projectile can achieve the same range $R$ for two angles of projection. If $t_1$ and $t_2$ are the times of flight in the two cases, then:

  • $t_1 t_2 \propto R^2$
  • $t_1 t_2 \propto R$✔️
  • $t_1 t_2 \propto \dfrac{1}{R}$
  • $t_1 t_2 \propto \dfrac{1}{R^2}$
Correct Answer Explanation

The two angles giving the same range are $\theta$ and $(90°-\theta)$.

$t_1 = \dfrac{2u\sin\theta}{g}$, $\quad t_2 = \dfrac{2u\cos\theta}{g}$

$t_1 t_2 = \dfrac{4u^2\sin\theta\cos\theta}{g^2} = \dfrac{2u^2\sin2\theta}{g^2} = \dfrac{2R}{g}$

Therefore $t_1 t_2 \propto \mathbf{R}$