In Game 3 of the 1970 NBA championship series, the L.A. Lakers were down by
two points with three seconds left in the game. The ball was inbounded to Jerry
West, whose image is silhouetted in today's NBA logo. He launched and made a
miraculous shot from beyond midcourt, a distance of 60 feet, to send the game into
overtime (there was no 3-point line at that time).
Through careful analysis of the game tape, one could determine the height at
which Jerry West released the ball, as well as the amount of time that elapsed
between the time the ball left his hands and the time the ball reached the basket.
This information could then be used to write a rule for the ball's height h in feet
as a function of time in flight t in seconds.
a. Suppose the basketball left West's hands at a point 8 feet above the ground.
What does that information tell about the rule giving h as a function of t?
b. Suppose also that the basketball reached the basket (at a height of 10 feet)
2.5 seconds after it left West's hands. Use this information to determine the
initial upward velocity of the basketball.
c. Write a rule giving h as a function of t.
