Question

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

• A. $1/R^2$
• B. $1/R$
• C. $R$
• D. $R^2$

Answer 1

The correct option is C $R$

We know that

Range $R=\frac{4^2\sin 2\theta }{9}$

If we put $\theta \to 90-\theta$

We get

$R=u^2\frac{\sin 2(90-\theta )}{9}=\frac{4^2\sin 180-2\theta }{29}$

$R=\frac{4^2\sin 2\theta }{29}$

Both ranges $\theta$ & $90-\theta$ are same

So $\cos \theta$ $T=\frac{24\sin \theta }{9}$; time of f light

we may write $t_1=\frac{24\sin \theta }{9}$

$\theta \to 90-\theta$

$t_2=\frac{24\sin (90-\theta )}{9}=\frac{24\cos \theta }{9}$

$\Rightarrow t_1{t}_2=\frac{{24}^{2}2\sin \theta \cos \theta }{9^2}$

$=\frac{2}{9}\cdot \frac{4^2\sin 2\theta }{9}=\frac{2}{9}R$.

$\Rightarrow t_1{t}_2\propto R$.