Chapter 14.5, Problem 77E

Parabolic trajectory Consider the parabolic trajectory

$x=(V_0\cos \alpha )t,y=(V_0\sin \alpha )t-\frac{1}{2}g{t}^2,$

where V₀ is the initial speed, α is the angle of launch, and g is the acceleration due to gravity. Consider all times [0, T] for which y ≥ 0.

1. a. Find and graph the speed, for 0 ≤ t ≤ T.
2. b. Find and graph the curvature, for 0 ≤ t ≤ T.
3. c. At what times (if any) do the speed and curvature have maximum and minimum values?