c The ball follows a parabolic path from the time it is hit to the moment it touches the ground.
A
a After 5 seconds
B
b 100 feet
C
c All t such that 0 ≤ t ≤ 5
Practice makes perfect
a The ball hit by the golfer will land on the ground when h=0. Therefore, we want to find the x-intercept of the equation that represents the ball's path. By equating it with 0, we can solve for the x-intercepts with the Zero Product Property.
At t=0 the ball leaves the ground, and when t=5 the balls land on the ground.
b A parabola is symmetrical. Therefore, if we can find two points on the graph that are on the same h-coordinate, they are going to be halfway from the parabola's vertex, which in this case describes the highest point of the golf ball. Two such points are the t-intercepts, which both lie on t=0.
Average: 0+5/2=2.5The maximum height occurs when t=2.5. Therefore, by substituting these values in the formula, we can find the maximum height of the golf ball.
The maximum height of the golf ball is 100 feet. We can see this situation on the following diagram.
c The ball follows a parabolic path from the moment it is hit to the moment it touches the ground. In Part A we have shown that the ball leaves the ground at t=0 to land back on it at t=5. Therefore, only times t between these two moments should be in our domain.
