Question

A Projectile can have the same range $R$ for two angles of projection. If $t_1$ and $t_2$ be the times of flights in the two cases, then the product of the two times of flights is proportional to

• A.
• B.
• C. 1/R
• D. R

Answer 1

The correct option is D $R$

We know that projectile has same range for complementary angles $\theta$ and ${90}^{\circ }-\theta$.
The time of flight for two cases be
$t_1=\frac{2u\sin \theta }{g}$ and $t_2=\frac{2u\sin ({90}^{\circ }-\theta )}{g}=\frac{2u\cos \theta }{g}$

$\Rightarrow t_1{t}_2=\frac{2u^2\sin 2\theta }{g^2}=\frac{2R}{g}$

Hence, option $\left(\text{D}\right)$ is the right choice.