Question

Two bodies are projected from the ground with same speed. If the angle of the projection from the ground is ${30}^{o}and{60}^o$ respectively, what is the ratio of their horizontal displacement after 2 s?

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

Answer 1

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

Let the velocity of projectiles be $u$.

For first projectile, $\theta ={30}^o$

Initial velocity in horizontal direction is $u\cos {30}^o$

Horizontal displacement after 2 seconds, $S_1=u\cos {30}^o\times t=u\times \frac{\sqrt{3}}{2}\times 2=\sqrt{3}u$

For second projectile, $\theta ={60}^o$

Initial velocity in horizontal direction is $u\cos {60}^o$

Horizontal displacement after 2 seconds, $S_2=u\cos {60}^o\times t=u\times \frac{1}{2}\times 2=u$

Thus ratio $\frac{S_1}{S_2}=\frac{\sqrt{3}}{1}$