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)

$h_{max.}=\frac{v^{2}si{n}^2\theta }{2g}$
as $h_{max.}$ is same in both the cases
$v_1^2\frac{si{n}^2{\theta }_1}{\text{2g}}={\text{v}}_2^2\frac{{\text{sin}}^2{\theta }_2}{\text{2g}}$
But ${\theta }_1=60^{\text{ο}}$ , ${\theta }_2=30^{\text{ο}}$
$v_1^2\frac{\left(\frac{3}{4}\right)}{g}={\text{v}}_2^2\frac{\left(\frac{1}{4}\right)}{\text{g}}$
$\frac{{\text{v}}_1}{{\text{v}}_2}=\frac{1}{\sqrt{3}}$