Question

If angles of projection are $(\frac{\pi }{4}+\theta )$ and $(\frac{\pi }{4}-\theta )$ where $\theta <\frac{\pi }{4}$, then the ratio of horizontal range described by the projectile is (speed is same):

• A. $2:1$
• B. $1:2$
• C. $1:1$
• D. $2:3$

Answer 1

The correct option is C $1:1$

${\theta }_1=(\frac{\pi }{4}+\theta )$

${\theta }_2=(\frac{\pi }{4}-\theta )$

$R=\frac{u^2\sin 2{\theta }_1}{g}=\frac{u^2\sin \left(\right(\pi /2)+2\theta )}{g}$

$=\frac{u^2\cos 2\theta }{g}$

$R=\frac{u^2\sin 2{\theta }_2}{g}=\frac{u^2\sin \left(\right(\pi /2)-2\theta )}{g}$

$=\frac{u^2\cos 2\theta }{g}$

Ratio will be $1:1$