Randall D. Knight — Dynamics II: Motion in a Plane: Problem 68

In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a \(45^{\circ}\) angle. Suppose a projectile of mass \(m\) is launched with speed \(v_0\) into a headwind that exerts a constant, horizontal retarding force \(\vec{F}_{\text{wind}} = -F_{\text{wind}}\hat{i}\). a. Find an expression for the angle at which the range is maximum. b. By what percentage is the maximum range of a \(0.50 \text{ kg}\) ball reduced if \(F_{\text{wind}} = 0.60 \text{ N}\)?