Golfing Project

By: Erica Nah and Anjali Patel

1. y= -16t^2+100t

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

The independent variable is the time in seconds and the dependent variable is the height in feet.

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

Domain: 0<x<6.25

Range: y<156

4. How long is golf ball in the air?

6.25 seconds

5. What is the maximum height of the ball?

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

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

154 feet, yes at 2.75 seconds
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8. At approximately what time is the ball 65 feet in the air? Explain.

At .7 seconds, the ball was 65 feet in the air. The height it travels up depends on the time.
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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 (hint: linear). When will he be at the same height as your ball? What is that height? Graph your scenario.

Height: 24 feet, 6 seconds
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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 how will Gloria's ball go? Compare the two shots graphically.

Gloria's golf ball hit the ground first by 1.3 seconds. Gloria's ball went 100ft high. The blue lines is Gloria's ball and the purple line is Earls ball.
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11. Suppose that Earl hit the second ball from a tee that was elevated 20 degrees above the fairway.

The higher the ball gets, the longer it take to reach the ground.

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

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

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

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

c. Graph the new relationship between the 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.

Red: y=-16t^2+100t+20

Blue: y=-16t^2+100t

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

Domain: x<6.25

Range: y<225