Chapter 5.7, Problem 44ES

Assume that a free-fall model applies. Solve these exercises by applying Formulas $\left(15\right)$ and $\left(16\right)$ . In these exercises take $g=32{\text{ ft/s}}^{\text{2}}$ or $g=9.8{\text{ m/s}}^{\text{2}}$ , depending on the units.

(a) Use the results in Exercise $43$ to make a conjecture about the relationship between the initial and final speeds of a projectile that is launched upward from ground level and returns to ground level.

(b) Prove your conjecture.