Question

Two bodies are projected with the same velocity. If one is projected at an angle of $30°$ and the other at an angle of $60°$ to the horizontal, find the ratio of the maximum heights reached.

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{5}$
• D. $\frac{1}{9}$

Answer 1

The correct option is B

$\frac{1}{3}$

The explanation for the correct option:

Step 1: Given data

The angle of projection for the first body, ${\theta }_1={30}^{°}$

The angle of projection for the second body, ${\theta }_2=60°$

Step 2: To find

We have to find the ratio of the maximum heights.

Step 3: Calculate the ratio of maximum heights

The formula of maximum height is given by

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

Here,

$\theta$ is the angle with respect to the horizontal surface.

$u$ is the initial velocity.

$g$ is the gravitational acceleration.

It is mentioned that both the bodies are projected with the same velocity therefore, the initial velocity will be equal for both bodies.

The value of acceleration due to gravity remains constant for every object and also they are projected with same initial velocity therefore. $H\propto {\sin }^2\theta$

$$\begin{gathered} \frac{H_1}{H_2}=\frac{{\sin }^2{\theta }_1}{{\sin }^2{\theta }_2} \\ =\frac{{\sin }^{2}30°}{{\sin }^{2}60°} \\ =\frac{1}{3} \end{gathered}$$

Hence, Option(B) is correct.