Question

Two projectiles thrown from the same point at angles $60^\circ $ and $30^\circ $ with the horizontal attain the same height. The ratio of their initial velocities is

• A. $1$
• B. $2$
• C. $\sqrt{3}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

Answer: (D)

$h_{m a x .}=\frac{v^{2} sin^{2} \theta }{2 g}$
as $h_{m a x .}$ is same in both the cases
$v_{1}^{2}\frac{sin^{2} \theta_{1}}{\text{2g}}=\text{v}_{2}^{2}\frac{\text{sin}^{2} \theta_{2}} {\text{2g}}$
But $\theta_{1}=60^{\text{ο}}$ , $\theta_{2}=30^{\text{ο}}$
$v_{1}^{2} \frac{\left(\frac{3}{4}\right)}{g} = \text{v}_{2}^{2} \frac{\left(\frac{1}{4}\right)}{\text{g}}$
$\frac{\text{v}_{1}}{\text{v}_{2}} = \frac{1}{\sqrt{3}}$