Chapter 5.7, Problem 42ES

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.

In $1939$ , Joe Sprinz of the San Francisco Seals Baseball Club attempted to catch a ball dropped from a blimp at a height of $800\text{ ft}$ (for the purpose of breaking the record for catching a ball dropped from the greatest height set the preceding year by members of the Cleveland Indians).

(a) How long does it take for a ball to drop $800\text{ ft}$ ?

(b) What is the velocity of a ball in miles per hour after an $800\text{ ft}$ drop $\left(88\text{ ft/s}=60\text{ mi/h}\right)$ ?

[Note: As a practical matter, it is unrealistic to ignore wind resistance in this problem; however, even with the slowing effect of wind resistance, the impact of the ball slammed Sprinz’s glove hand into his face, fractured his upper jaw in $12$ places, broke five teeth, and knocked him unconscious. He dropped the ball!]