All categories - 5 October 2007

You and your friend are playing tennis. Your friend lobs the ball high into the air, hitting it 3 feet above the court with an initial vertical velocity of 40 feet per second. You back up and prepare to hit an overhead smash to win the point.
a.) Use the model h=-16t^2 + v0t + h0 to write an equation giving the height of the lobbed tennis ball as a function of time.
b.) At what time t does the ball reach its maximum height above the court? What is the maximum height?
c.) If you plan to hit the smash when the ball falls to a height of 8 feet above the court, how long do you have to prepare for the shot?
d.) If you plan to hit the smash when the ball is between 6 feet and 9 feet above the court (inclusive) what are your possible preparation times?
e.) Suppose you hit the smash when the ball is 8 feet above the court. It takes 0.1 second for the ball you smashed to hit the court on your friend's side of the net. What was the ball's initial velocity coming off your racket?

THANKS!

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