Question

A ball is projected at an angle of ${30}^o$ and ${60}^o$ to the horizontal with the same initial velocity in each case. The ratio of ranges is
$(g=10m{s}^{-2})$

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

Answer 1

The correct option is A $1:1$

Range $\propto \sin 2\theta$
$\Rightarrow \sin 2\left({30}^0\right)=\frac{\sqrt{3}}{2}$
$\sin 2\left({60}^0\right)=\frac{\sqrt{3}}{2}$

$\Rightarrow \frac{R_1}{R_2}=\frac{\sin 60}{\sin 120}=\frac{1}{1}=\underset{–}{1:1}$