Chapter 13.P, Problem 7P

If a projectile is fired with angle of elevation $\alpha$ and initial speed $\nu$, then parametric equations for its trajectory are

$x=\left(\nu \text{ cos }\alpha \right)t$

$y=\left(\nu \text{ sin }\alpha \right)t-\frac{1}{2}g{t}^2$

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