Question

The range of a projectile when launched at angle $\theta$ is same as when launched at angle $2\theta$. What is the value of $\theta$?

• A. ${15}^o$
• B. ${30}^o$
• C. ${45}^o$
• D. ${60}^o$

Answer 1

Answer: (B)

${30}^o$

Range of a projectile launched at an angle $\theta$ is given as $R=\frac{u^{2}sin2\theta }{g}$

$R\left(\theta \right)=R\left(2\theta \right)$

$⟹\frac{u^{2}sin2\theta }{g}=\frac{u^{2}sin4\theta }{g}$

$⟹sin2\theta =sin4\theta =2sin2\theta cos2\theta$

$⟹cos2\theta =\frac{1}{2}$

$⟹2\theta ={60}^{\circ }$

$⟹\theta ={30}^{\circ }$