For problem 4, use the position function p() = 162 + 0 + p0, where s is measured in feet, t in seconds and 0 and p0 are the initial velocity and position respectively.

4. A professional baseball pitcher was capable of throwing a baseball 160 ft/s. During his career, he had the opportunity to pitch in the Houston Astrodome. The Astrodome was an indoor stadium with a ceiling 208 ft. high.

Could the pitcher have hit the ceiling of the Astrodome if he were capable of giving a baseball an upward velocity of 100 ft/s from a height of 7.5 ft?

How fast would the pitcher have to throw a ball upward from a height of 7.5 feet in order to hit the ceiling of the Astrodome?