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, then what is the product of two times of flight?

• A. $t_1{t}_2\propto \frac{1}{R^2}$
• B. $t_1{t}_2\propto R^2$
• C. $t_1{t}_2\propto \frac{1}{R}$
• D. $t_1{t}_2\propto R$

Answer 1

The correct option is D $t_1{t}_2\propto R$

The horizontal range is the same for the angles of projection $\theta$ and $({90}^{\circ }-\theta )$

$t_1=\frac{2u\sin \theta }{g}$

$t_2=\frac{2u\sin ({90}^{\circ }-\theta )}{g}$

$=\frac{2u\cos \theta }{g}$

Now,

$t_1{t}_2=\frac{2u\sin \theta }{g}\times \frac{2u\cos \theta }{g}=\frac{2}{g}\left[\frac{u^{2}sin2\theta }{g}\right]$

$=\frac{2}{g}R$

Final answer: (b)