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. Ratio of their time of flight is

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

Answer 1

The correct option is C $1:\sqrt{3}$

time of flight $T=\frac{2v_{0}sin\theta }{g}$

$\frac{T_1}{T_2}=\frac{2v_{0}sin{30}^{\circ }}{g}\times \frac{g}{2v_{0}sin{60}^{\circ }}$

$\frac{T_1}{T_2}=\frac{sin{30}^{\circ }}{sin{60}^{\circ }}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}$