Question

Galileo writes that for angles of projection of projectile at angle $(45+\alpha {)}^{\circ }$ and $(45-\alpha {)}^{\circ }$ the horizontal ranges described by the projectile are in the ratio of

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

Answer 1

The correct option is C $1:1$

$R_1=\frac{u^{2}sin2({45}^{\circ }+\alpha )}{g}=\frac{u^{2}cos2\alpha }{g}$

$R_2=\frac{u^{2}sin2({45}^{\circ }-\alpha )}{g}=\frac{u^{2}cos2\alpha }{g}\Rightarrow R_1=R_2$