Question

For a given velocity, a projectile has the same range R for two angles of projection. If t₁ and t₂ are the times of flight in the two cases then

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

Answer 1

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

For same range angles 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 = $t_1{t}_2$ = $\frac{4u^{2}sin\theta cos\theta }{g^2}$
$t_1{t}_2$ = $\frac{2}{g}$ $\frac{\left(u^{2}sin2\theta \right)}{g}$ = $\frac{2R}{g}$ $\Rightarrow$ $t_1{t}_2$ $\alpha$ R