Question

If Rand H represent the horizontal range and the maximum height achieved by a projectile then which of the relation exists?

• A. $\frac{H}{R}=4\cot \theta$
• B. $\frac{R}{H}=4\cot \theta$
• C. $\frac{H}{R}=4\tan \theta$
• D. $\frac{R}{H}=4\tan \theta$

Answer 1

The correct option is B $\frac{R}{H}=4\cot \theta$

$R=\frac{u^2\sin 2\theta }{g}=\frac{2u^2\sin \theta .\cos \theta }{g}$

$H=\frac{u^2{sin}^2\theta }{2g}$

$\therefore \frac{H}{R}=\frac{u^2{sin}^2\theta }{g}\times \frac{g}{2u^2\sin \theta .\cos \theta }$

$=\frac{\sin \theta }{4\cos \theta }$

$\Rightarrow \frac{R}{H}=\frac{4\cos \theta }{\sin \theta }or,\frac{R}{H}=4\cot \theta$