Golf Algebra Project
GOLF GOLF GOLF
Graph this function f(t) = -16t2 + 100t
What are the independent and dependent variables in this situation?
Independent: Time (x or t) Dependent: Height (y or f(t))
What is a reasonable domain and range for this function?
Domain - all reals, range - y ≤156.25
How long is the golf ball in the air?
What is the maximum height of the ball?
How long after it is hit does the golf ball reach the maximum height?
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 . The ball is also at the same height at 2.5 seconds.
At approximately what time is the ball 65 feet in the air? Explain.
0.74/0.75 seconds. We calculated using G-solve (x-cal)
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 scenario.
He will be at the same height as the ball at 6 seconds and 24 feet in the air.
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) = -16t2 + 80t. Earl hits a shot off the tee that has a height modeled by the function f(t) = -16t2 + 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 at 5 seconds , and it will reach 100 feet in altitude. It will also be 1.25 seconds faster than Earl's ball.
Red is Gloria, Green is Earl.
Suppose the 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?
It would increase the elevation by a significant amount.
b. Write a function that describes the new path of the ball.
f(x) = -16x2 + 120x
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.
Time doesn’t change, it does not increase or decrease. Only the air altitude increases, from the maximum being 156.25 feet, to 225 feet.
Original Trajectory (Earl)
This is the original height of the ball.
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Earl's is higher now
See how the green ball was lifted up higher? The new path's equation is: f(x) = -16x2 + 120x
d. What would be a reasonable domain and range of this new function?
Domain- x= all reals Range- y≤ 225