A golfer is standing directly behind a tree, and decides to try to hit the golf ball over the tree. The path of his golf ball can be modeled by the function h = -t² + 81 + 24, where h is the golf ball's height (in feet) and t is the time it has been in the air (in seconds).

a) How long will it take the golf ball to reach its highest point?
b) If the tree in front of the golfer is 23 feet tall, will the shot be able to clear it?
c) When will the ball hit the ground?