Suppose a punter kicks a football so that the upward component of its velocity is 80 feet per second. If the ball is 3 feet off the ground when it is kicked, then the height of the ball, in feet, t seconds after it is kicked is given by h(t) = 3 + 80t - 16t2.
a. Find the upward velocity v(t) of the football.
b. How fast is the ball travelling upward 1 second after it is kicked?
c. Find the time when the ball reaches its maximum height.
d. What is the maximum height of the ball?