Answer to Question #258147 in Calculus for Latha

Question

When the air resistance is ignored, the horizontal range R of a projectile is given by R(8)= 9 sin 20 where is the constant initial velocity, g is the acceleration due to gravity, and is the angle of elevation or departure. Find the maximum range of projectile.

Answer 1

In general, the horizontal range $R$ of a projectile is given by $R(\alpha)=\frac{v_0^2\cdot\sin2\alpha}{g}$ .

The maximum range of projectile will be when $\sin2\alpha=1\to \alpha=45°$

$R_{max}(\alpha)=R_{max}(45°)=\frac{v_0^2}{g}$ .