Chapter 1.3, Problem 81E

Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h = f(t) = 64t − 16t², where t is measured in seconds after the hit

1. a. Is this function one-to-one on the interval 0 ≤ t ≤ 4?
2. b. Find the inverse function that gives the time t at which the ball is at height h as the ball travels upward. Express your answer in the form t = f⁻¹ (h).
3. c. Find the inverse function that gives the time t at which the ball is at height h as the ball travels downward. Express your answer in the form t = f⁻¹ (h).
4. d. At what time is the ball at a height of 30 ft on the way up?
5. e. At what time is the ball at a height of 10 ft on the way down?