Question

The horizontal range of an oblique projectile is four times the maximum height attained by the projectile. The angle of projection is

• A. $45°$
• B. $30°$
• C. $60°$
• D. $90°$

Answer 1

The correct option is A

$45°$

Step 1: Given data

Range,$R$=$4H$ ($H$is the maximum height)

Step 2: Formula used

The mathematical expression for the horizontal range is given by :

Range, $R=\frac{u^2\sin 2\theta }{g}$ where $u$ is the velocity of projectile, and $\theta$ is the angle of projection.

The mathematical expression for the maximum height is given by :

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

Step 3: Find the angle of projection

According to Question:

$\frac{u^2}{g}\sin 2\theta$$=\frac{4u^2{\sin }^2\theta }{2g}$

$$\begin{gathered} \Rightarrow \sin 2\theta =2{\sin }^2\theta \\ \Rightarrow 2\sin \theta .\cos \theta =2{\sin }^2\theta \\ \Rightarrow \cos \theta =\sin \theta \\ \Rightarrow \theta =45° \end{gathered}$$

Hence, the angle of projection is $45°$

Thus, option A is the correct answer.