Question

A particle is projected with a velocity of $30\text{m/s}$ at two angles of ${30}^{\circ }$and ${60}^{\circ }$ respectively. Then the ratio of their times of flight is

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

Answer 1

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

$\text{Time of flight,}T=\frac{2u\sin \theta }{g}{T}_1=\frac{2u\sin {30}^{\circ }}{g}\text{and}{T}_2=\frac{2u\sin {60}^{\circ }}{g}$
Hence $\frac{T_1}{T_2}=\frac{\sin {30}^{\circ }}{\sin {60}^{\circ }}\frac{T_1}{T_2}=\frac{1}{\sqrt{3}}$