Question

Two projectiles are projected with the same velocity. If one is projected at an angle of ${30}^o$ and the other at ${60}^o$ to the horizontal. The ratio of maximum heights reached, is

• A. $1:3$
• B. $1:2$
• C. $2:3$
  
• D. $3:1$
  

Answer 1

Answer: (A)

$1:3$

When a projectile is projected with a velocity, $u$ and at angle, $\theta$ to the horizontal, the maximum height reached by the projectile is given by,

$H=\frac{u^2{\sin }^2\theta }{2g}$

As both projectiles have same projected velocity, so

$H\propto {\sin }^2\theta$

Thus ratio of maximum heights $\frac{H_{30}}{H_{60}}=\frac{{\sin }^{2}30}{{\sin }^{2}60}=\frac{1/4}{3/4}=1/3$