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Question

For a given velocity, a projectile has the same range $$R$$ for two angles of projection if $$t_1$$ and $$t_2$$ are the time of flight in the two cases, then:


A
t1t2R
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B
t1t2R2
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C
t1t21R2
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D
t1t21R
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Solution

The correct option is B $$t_1t_2\propto R$$
The range of a projectile motion is given as $$R=\dfrac{2u^2 sin\theta cos\theta}{g}$$
It two projectiles with same velocity have same range,
$$R=\dfrac{2u^2sin\theta_1cos\theta_1}{g}=\dfrac{2u^2 sin\theta_2cos\theta_2}{g}$$
$$\implies \theta_2=90^{\circ}-\theta_1$$
Thus, the times of the flights are:
$$t_1=\dfrac{2usin\theta_1}{g}$$
$$t_2=\dfrac{2usin\theta_2}{g}=\dfrac{2ucos\theta_1}{g}$$
Thus, $$t_1t_2\propto sin\theta_1cos\theta_1\propto R$$

Physics

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