By: Katie Austin, Ashley Miznazi, Steve Koshy
WE ♡ MATH
1) GRAPH f(t)=-16t²+100t
The settings are
X min: 0
X max: 7
Y min: 0
Y max: 250
(this applies to all graphs)
2) What are the independent and dependent variables in this situation?
DV: Height in feet
The independent variable (x) is time, because the height (y) changes as a result of how long it has been since the golf ball was hit, or the time.
3) What is a reasonable domain and range for this project?
This is good because it is the smallest and largest values for time before the golf ball hits the ground, but after it has been hit. (0 is the takeoff, 6.25 is the landing)
range: 0 ≤ y ≤ 156.25
This is a good range because it is the highest and lowest representative values the ball will be in the air. (0 is on the ground, 156.25 is the vertex)
4) How long is the golf ball in the air?
5) What is the maximum height of the ball?
6) How long after it is hit does the golf ball reach the maximum height?
You can tell this because at the max, the x value, or time, is 3.125. Rounded it is 3.13
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?
8) At approximately what time is the ball 65 feet in the air? Explain.
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 scenario.
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)=-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. Gloria’s hits after 5 seconds. Earl’s hits after 6.25 seconds. If you subtract these, you get that hers hits 1.25 seconds sooner. Gloria’s ball will go to 100 feet. Earl's will go to 154 feet. His is 54 feet higher. Gloria's Graph below is the red one. Earl's is blue.
11. 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 goes for 6.44 seconds instead of just 6.25 seconds. Its new max is 176.25 feet. It is taller, and lasts for a few more fractions of a second. (0.19 seconds, to be exact) The graph would shift up, or get taller, 20 units.
b. Write a function that describes the new path of the ball.
-16x ² +100x+20
The number at the top is the new function, and you add 20 feet because he is 20 feet in the air. It goes higher and longer
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?
0 ≤ x ≤ 6.44
This is good because it is the smallest and largest values for time before the golf ball hits the ground, but after it has been hit. (0 is the takeoff, 6.44 is the landing)
0 ≤ y ≤ 176.25
This is a good range because it is the highest and lowest representative values the ball will be in the air. (0 is on the ground, 176.25 is the vertex)