Projectile Range at Different Angles – Rankers Physics
Topic: Kinematics
Subtopic: Ground to Ground Projectile

Projectile Range at Different Angles

The range of a projectile, when launched at an angle of \(15^\circ\) with the horizontal is \(1.5\text{ km}\). What is the range of the projectile when launched at an angle of \(45^\circ\) to the horizontal?
\(1.5\text{ km}\)
\(3\text{ km}\)
\(6\text{ km}\)
\(0.75\text{ km}\)

Solution:

Range is given by \(R = \frac{u^2 \sin(2\theta)}{g}\). For \(\theta = 15^\circ\), \(R_1 = \frac{u^2 \sin(30^\circ)}{g} = 1.5\text{ km}\) which implies \(\frac{u^2}{g} = 3.0\text{ km}\). For \(\theta = 45^\circ\), \(R_2 = \frac{u^2 \sin(90^\circ)}{g} = \frac{u^2}{g} = 3\text{ km}\).

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