The maximum height attained by projectile is increased by 10 % by… - Vidyadip

MCQ

The maximum height attained by projectile is increased by $10 \%$ by changing the angle of projection, without changing the speed of projection. The percentage increase in the time of flight will be

A
$20 \%$
B
$15 \%$
C
$10 \%$
✓
$5 \%$

✓

Answer

Correct option: D.

$5 \%$

(D)
$H =\frac{ u ^2 \sin ^2 \theta}{2 g}$
Differentiating prartially,
$\delta H =\frac{ u ^2(2 \sin \theta \cdot \cos \theta) \delta \theta}{2 g}$
$\therefore \quad \frac{\delta H }{ H }=\frac{2 \cos \theta \delta \theta}{\sin \theta}=0.1$ (given)
Similarly, $\frac{\partial I}{T}=\frac{\cos \theta \partial \theta}{\sin \theta}=0.05$
Therefore, T increases by 5%

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