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
B
t1t2R2
C
t1t21R2
D
t1t21R

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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