A projectile thrown from the ground has initial speed ' u ' and i… - Vidyadip

MCQ

A projectile thrown from the ground has initial speed ' $u$ ' and its direction makes an angle ' $\theta$ ' with the horizontal. If at maximum height from ground, the speed of projectile is half its initial speed of projection, then the maximum height reached b the projectile is [ $g=$ acceleration due to gravity, $\sin 30^{\circ}=\cos 60^{\circ}$ $=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2$ ]

A
$\frac{u^2}{g}$
B
$\frac{u^4}{2 g}$
C
$\frac{2 u^2}{g}$
✓
$\frac{3 u^2}{8 g}$

✓

Answer

Correct option: D.

$\frac{3 u^2}{8 g}$

(d) : At maximum height, $u \cos \theta=\frac{1}{2} u$
$
\Rightarrow \cos \theta=\frac{1}{2} \Rightarrow \theta=60^{\circ}
$
Maximum height, $H=\frac{u^2 \sin ^2 \theta}{2 g}=\frac{u^2 \sin ^2 60^{\circ}}{2 g}=\frac{3 u^2}{8 g}$

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