Question

If $R$ and $h$ represent the horizontal range and maximum height respectively of an oblique projectile, then $\frac{R^2}{8h}+2h$ represents

• A. Maximum horizontal range
• B. Maximum verticle range
• C. Time of flight
• D. Velocity of projectile at highest point.

Answer 1

The correct option is A Maximum horizontal range

We know that, $R=\frac{v^2\sin 2\theta }{g}......\text{(i)}$
and $h=\frac{v^2{\sin }^2\theta }{2g}$
$\Rightarrow \frac{R^2}{8h}=\frac{v^2\left(2\sin \theta \cos \theta \right)}{g}\times \frac{v^2\left(2\sin \theta \cos \theta \right)}{g}\times \frac{2g}{8v^2{\sin }^2\theta }$
$=\frac{v^2{\cos }^2\theta }{g}$
Now, $\frac{R^2}{8h}+2h=\frac{v^2{\cos }^2\theta }{g}+\frac{v^2{\sin }^2\theta }{g}=\frac{v^2}{g}$
Using eq. $\text{(i)}$, we can say
$\frac{v^2}{g}$ is the maximum horizontal range of an oblique projectile.