Golfing Project

By: Brett Henry

2. What are the independent and dependent variables in this situation?

The independent variable is the time (in seconds).

The dependent variable is the height (in feet).

3. What is a reasonable domain and range for this function?

A reasonable domain and range would be: D: {0<x<8}; R: {0<y<175};

4. How long is the golf ball in the air?

The ball is in the air for 6.25 seconds.

5. What is the maximum hight of the ball?

The maximum height of the ball is 156.25 feet.

6. How long after it is hit does the ball reach the maximum height?

After 3.125 seconds the ball is at its maximum height.

7. What is the height of the ball at 3.5 seconds? Is there another time at which the ball is at this same height? If so, when?

When the ball has traveled for 3.5 seconds the ball is at a height of 154 feet. Yes there is another time at which the ball is at the same height, at 2.75 seconds.

8. At approximately what time is the ball 65 feet in the air? Explain.

The ball is 65 feet in the air at approximately .74 seconds and 5.5 seconds. Both of which are correct because the graph, being a parabola, goes up and down, meaning for several different Y values there are two matching X values.

9. Tweety Bird takes off from the green at the same time you tee off. His height is increasing at a rate of 4 feet per second. When will he be at the same height as your ball? What is that height? Graph this senario.

At 6 seconds Tweety Bird will be at the same height as the ball. This height is 24 feet.

10. Suppose Gloria and Earl stand side bt side and teed off at the same time. The height of Gloria's ball is modeled by the function f(t) = -16t^2 + 80t. Earl his a shot off the tee that has a height modeled by the function f(t) = -16t^2 +100t. Whos golf ball will hit the ground first? How much sooner does it hit the ground? How high will Gloria's ball go? Compare the two shots graphically

Gloria's ball will hit the ground first. Gloria's ball will hit the ground after 5 seconds which is 1.25 seconds earlier than Earl's. Gloria's ball's maximum height is 100 feet.

11. Suppose that Earl hit a second ball from a tee that was elevated 20 feet above the fairway.

a. What effect would the change in elevation have on the graph?

The ball would start at 20 feet on the Y-axis and that would cause the ball to fall 20 more feet, increasing the time and max height of the graph.

b. Write a function that describes the new path of the ball.

f(t) = -16t^2 + 100t + 20

c. Graph the new relationship between height and time. Make sure to label the graph and to graph the original function as well as the new function in the given graph.

d. What would be a reasonable domain and range of this new function?

D: {0<x<185}; R: {0<y<8}