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Question

A projectile can have the same range $$R$$ for two angles of projection. If $$t_{1}$$ and $$t_{2}$$ be the times of flight in the two cases:


A
t1t2R2
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B
t1t2R
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C
t1t21R
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D
t1t21R2
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Solution

The correct option is A $$\displaystyle t_{1}t_{2} \propto R$$
$$R = \dfrac{v^2 sin 2\theta_1}{g} = \dfrac{v^2 sin 2\theta_2}{g}$$

$$t_1 = \dfrac{2vsin \theta_1}{g}$$          $$t_2 = 2\dfrac{v sin \theta_2}{g}$$

assume if $$\theta_1 = \dfrac{\pi}{2} - \theta_2$$

then $$t_2t_2 = \dfrac{4v^2sin \theta_1 sin(\dfrac{\pi}{2} -\theta_1)}{g^2} = \dfrac{2v^2 \times 2 sin\theta_1 cos\theta_1}{g^2} = \dfrac{2}{g}\dfrac{v^2sin2\theta_1}{g} = \dfrac{2}{g}R$$

Physics

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