A projectile is fired from level ground at an angle above the hor… - Vidyadip

MCQ

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

A
$\tan \,\phi = \frac{1}{4}\,\tan \,\theta $
B
$\tan \,\phi = \tan \,\theta $
✓
$\tan \,\phi = \frac{1}{2}\,\tan \,\theta $
D
$\tan \,\phi = 2\,\tan \,\theta $

✓

Answer

Correct option: C.

$\tan \,\phi = \frac{1}{2}\,\tan \,\theta $

c
It is clear from the adjoining figure that,

$\tan \phi=\frac{\mathrm{H}}{\mathrm{R} / 2}$

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

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