Question

A projectile is fired from level ground at an angle $\theta$ above the horizontal. The elevation angle $\varphi$ of the highest point as seen from the launch point is related to $\theta$ by the relation:

• A. $tan\varphi =2tan\theta$
• B. $tan\varphi =tan\theta$
• C. $tan\varphi =\frac{1}{2}tan\theta$
• D. $tan\varphi =\frac{1}{4}tan\theta$

Answer 1

The correct option is C $tan\varphi =\frac{1}{2}tan\theta$

From fig

$\tan \varphi =\frac{H}{R/2}$

$=\frac{u^2{\sin }^2\theta /2g}{u^2\sin 2\theta /2g}=\frac{si{n}^2}{\sin 2\theta }=\frac{1}{2}\tan \theta$