Question

Two particles are projected from the same point with the same speed, at different angles ${\theta }_1$ and ${\theta }_2$ to the horizontal. Their times of flight are $t_1$ and $t_2$ and they have the same horizontal range. Then

• A. $\frac{t_1}{t_2}=\tan {\theta }_1$
• B. $\frac{t_1}{t_2}=\tan {\theta }_2$
• C. $\frac{t_1}{\cos {\theta }_2}=\frac{t_2}{\cos {\theta }_1}$
• D. ${\theta }_1+{\theta }_2={90}^{\circ }$

Answer 1

The correct option is A $\frac{t_1}{t_2}=\tan {\theta }_1$

Since both the projectiles have same range and same projectile speed. Thus if angle of projection of one projectile is ${\theta }_1$, angle of projection of second projectile is $90-{\theta }_1$.

Time of flight of first projectile $t_1=\frac{2u\sin {\theta }_1}{g}$

Time of flight of second projectile $t_2=\frac{2u\sin (90-{\theta }_1)}{g}=\frac{2u\cos {\theta }_1}{g}$

Ratio $\frac{t_1}{t_2}=\frac{\sin {\theta }_1}{\cos {\theta }_1}=\tan {\theta }_1$