Question

Galileo writes that for angles of projection of a projectile at angles $(45+\theta )and(45-\theta )$, the horizontal ranges described by the projectile are in the ratio of $(if\theta \le 45)$

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

Answer 1

The correct option is C 1 : 1

For angle $({45}^{\circ }-\theta ),R=\frac{u^{2}sin({90}^{\circ }-2\theta )}{g}=\frac{u^{2}cos2\theta }{g}$
For angle $({45}^{\circ }+\theta ),R=\frac{u^{2}sin({90}^{\circ }+2\theta )}{g}=\frac{u^{2}cos2\theta }{g}$