Chapter 3, Problem 81GP

(II) Here is something to try at a sporting event. Show that the maximum height h attained by an object projected into the air, such as a baseball, football, or soccer ball, is approximately given by

$h\approx 1.2t^{2}m,$

where t is the total time of flight for the object in seconds. Assume that the object returns to the same level as that from which it was launched, as in Fig. 3–42. For example, if you count to find that a baseball was in the air for t = 5.0 s, the maximum height attained was h = 1.2 × (5.0)² = 30 m. The beauty of this relation is that h can be determined without knowledge of the launch speed ${\upsilon }_0$ or launch angle ${\theta }_0$.

FIGURE 3–42 Problem 42.