Golf Activity Project

Karis and Surya

Background Info

The height h (in feet) above the ground of a golf ball depends on the time, t (in seconds) it has been in the air. Earl hits a shot off the tee that has a height modeled by the function
f(t)= −16t^2+ 100t

1. Graph the function f(t)= −16t^2+ 100t

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

The dependent variable is the height the ball is at while in the air and independent variable is how long the ball is in the air at a certain height.

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

Domain: all real numbers Range: y≤156.25

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

The ball is in the air for a total of 6.25 seconds

5. What is the maximum height of the ball?

The maximum height of the ball is 156.25ft at 3.125 seconds

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

The golf ball reaches the ground after 3.125 seconds

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?

The height of the ball at 3.5 seconds is 154ft. The other time when it is at this height is 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 0.74 seconds. Since the y is 65 feet, x would have to be 0.736 or 0.74 in order to make the graph match the equation.

9. Tweedy 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 scenario.

Tweedy will be at the same height as me when I am at 0 seconds, where the height is 0.

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 ! ! = −16!2 + 80! . Earl hits a shot off the tee that has a height modeled by the function ! !  = −16!! + 100!. 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.

Earl: 6.25,0
Gloria: 5,0
Gloria’s golf ball hit the ground first, by 1.25 seconds. Gloria’s ball’s tallest height (max) was 100ft at 2.5 seconds. Earl’s tallest height (max) was 156.25ft at 3.125 seconds

11. Suppose 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 height of the parabola will be taller and a bit wider

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

Y = -16x^2+100x+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?

Domain= 0≤X≤3.13

Range= 0≤Y≤ 176.25