Question

A body is projected with some initial velocity $u$ at angle $\frac{\pi }{7}$ with the horizontal. At what angle should another body be thrown so that the horizontal range in both cases is the same?

• A. $\frac{\pi }{2}$
• B. $\frac{5\pi }{14}$
• C. $\frac{4\pi }{7}$
• D. $\frac{6\pi }{7}$

Answer 1

The correct option is B $\frac{5\pi }{14}$

For a particle projected at an angle $\theta$, range of the particle is given by $\frac{2u^{2}sin\theta cos\theta }{g}$.

If one projects with an angle of $\frac{\pi }{2}-\theta$, the range of the particle will be, $\frac{2u^{2}sin(\frac{\pi }{2}-\theta )cos(\frac{\pi }{2}-\theta )}{g}$

i.e $=\frac{2u^{2}cos\theta sin\theta }{g}$.

For angles $=\theta$ and $\frac{\pi }{2}-\theta$, a projectile has the same range.

$\therefore$ For angle = $\frac{\pi }{2}-\frac{\pi }{7}=\frac{5\pi }{14}$ the horizontal range will be the same.