Question

Figure shows the trajectory of a projections fired at an angle $\theta$ with the horizontal. The elevation angle of the highest point as seen from the point of launching is $\phi$. The relation between $\phi$ ans $\theta$ is

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

Answer 1

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

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

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

$\tan \varphi =\frac{H}{H_i}=\frac{{\sin }^2\theta }{\sin 2\theta }=\frac{1}{2}\tan \theta$