Question

A projectile thrown with an initial speed u and angle of projection 15^o to the horizontal has a range R. If the same projectile is thrown at an angle of 45^o to the horizontal with speed 2u, its range will be

• A. 12 R
• B. 3 R
• C. 8 R
• D. 4 R

Answer 1

Answer: (C)

8 R

Answer 2

$R = \frac{u^{2}\sin 2\theta}{g}$ $\therefore R \propto u^{2}\sin 2\theta$

$\frac{R_{2}}{R_{1}} = \left( \frac{u_{2}}{u_{1}} \right)^{2}\left( \frac{\sin 2\theta_{2}}{\sin 2\theta_{1}} \right)$

$\Rightarrow R_{2} = R_{1}\left( \frac{2u}{u} \right)^{2}\left( \frac{\sin 90^{o}}{\sin 30^{o}} \right) = 8R_{1}$