Example 3. Suppose a stone is thrown vertically upward with an initial velocity of 64 ft/sec from a bridge that is 80 feet above the river. The position function is given by s(t) = 16t^2 + 64t + 80, where s(t) measures the height (in feet) of the stone above the surface of the river, and t is measured in seconds.
a.) How high does the rock go?
b.) What are the velocity and speed of the rock when it is 128 feet above the ground and traveling up? What about when 128 feet above the ground and traveling down?
c.) What is the acceleration of the rock at any time t during its flight?
d.) What is the jerk of the rock at any time t during its flight?
e.) When does the rock hit the surface of the river?