Chapter 13, Problem 7P

If a projectile is fired with angle of elevation α and initial speed v. then parametric equations for its trajectory are $x=\left(v\cos \alpha \right)ty\text{ =}\left(v\sin \alpha \right)t-\frac{1}{2}g{t}^2$

(See Example 13.4.5.) We know that the range (horizontal distance traveled) is maximized when α =45^c. What value of α maximizes the total distance traveled by the projectile? (State your answer correct to the nearest degree.)