Question

Two projectiles are projected at angles $(\frac{\pi }{4}+\theta )\text{and}(\frac{\pi }{4}-\theta )$ with the horizontal, where $\theta <\frac{\pi }{4}$, with same speed. The ratio of horizontal ranges described by them is

• A. $\tan \theta :1$
• B. $1:{\tan }^2\theta$
• C. $1:1$
• D. $1:\sqrt{3}$

Answer 1

The correct option is C $1:1$

Since $\frac{\pi }{4}+\theta +\frac{\pi }{4}-\theta =\frac{\pi }{2}$

$R=\frac{u^2\sin 2\theta }{g}$
If the angles of projection of two projectiles are complimentary to each other than the range of both the projectiles are equal for a given velocity.
Hence, option (c) is correct