Golfing Project

By- Avery, Jacob, and Allan

1. Graph this function f(t)= -16t+100t

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

Independent- Time

Dependent- Height

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

Domain: 0 ≤ x ≥ 6.25

Range: y ≤ 156.25

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

6.25 seconds.

5. What is the maximum height of the ball?

156.25 ft

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

3.13 seconds, rounded to the nearest hundredth.

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?

At 3.5 seconds, the ball is at 154 ft. Also at 2.75 seconds, it is also at 154 ft.

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

0.74 seconds.

9. Tweety Bird takes off from the green 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 scenario.

At 6, 24... He will be at the same height as our ball. That's where it intercepts.

10. Suppose Gloria and Earl stand side by 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 hits a shot off the tee that has a height modeled by the function f(t)=-16t^2+100t. Whose 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 go up to 100 ft high and her ball will hit the ground 1.25 seconds before earls.

11a. Suppose that Earl hit a second ball from a tee that was elevated 20 feet above the fairway. What effect would the change in elevation have on the graph?

The ball will always be 20 ft above the original path.

11b. Write a function that describes the new path of the ball.

-16^2+100t +20

11c. Graph the new relationship between height time. Make sure to label the graph and to graph the original function as well as the new function in the given graph.

11d. What would be a reasonable domain and range of this new function?

Domain: 2 ≤ x ≥ 6.44

Range: y ≤ 176.25