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 times of flight in the two cases then

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

Answer 1

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

For same range angle of projection should be $\theta$ and $90-\theta$
So, time of flights $t_1=\frac{2usin\theta }{g}$ and
$t_2=\frac{2usin(90-\theta )}{g}=\frac{2ucos\theta }{g}$
By multiplying =$t_1{t}_2=\frac{4u^{2}sin\theta cos\theta }{g^2}$
$t_1{t}_2=\frac{2}{g}\frac{\left(u^{2}sin2\theta \right)}{g}=\frac{2R}{g}\Rightarrow t_1{t}_2\propto R$