Question

Two stones are projected from the same point with same speed making angles ${45}^o+\theta$ and ${45}^o-\theta$ with the horizontal respectively. If $\theta \le {45}^o$, then the horizontal ranges of the two stones are in the ratio of

• A. $1:1$
• B. $1:2$
• C. $1:3$
• D. $1:4$

Answer 1

The correct option is A $1:1$

Speed is same:$u_1=u_2$

Range is given by:$R=\frac{u^2\sin 2\theta }{g}$

$\frac{R_1}{R_2}=\frac{u^2\sin 2{\theta }_1}{g}\times \frac{g}{u^2\sin 2{\theta }_2}=\frac{\sin 2{\theta }_1}{\sin 2{\theta }_2}=\frac{\sin 2(45°+\theta )}{\sin 2(45°-\theta )}=\frac{\sin (90°+2\theta )}{\sin (90°-2\theta )}=\frac{\cos 2\theta }{\cos 2\theta }=\frac{1}{1}$