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 time of flights is proportional to :

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

Answer 1

The correct option is D $R$

'R' Range is same for two angles $\left(\theta \right)\&(90-\theta )$

Time of flight in these case are $t_1\&t_2$ respectively

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

$t_2=\frac{u\sin (90-\theta }{g}=\frac{u\cos \theta }{g}$

Product of $t_1\&t_2$

$t_1\times t_2=\frac{u\sin \theta \times u\cos \theta }{g^2}$

$t_1{t}_2=\frac{2u^2\sin \theta \times \cos \theta }{2g^2}=\frac{2}{g}\left(\frac{u^2\sin 2\theta }{g}\right)$

$t_1.t_2\alpha R$