With The Great Wasif & Noah
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. Round answers to the nearest hundredth when necessary.
Time is the independent and the height is the dependent
3. What is a reasonable domain and range for this function?
Domain= all real numbers
Range = y < 156
4. How long is the golf ball in the air?
The golf ball is in the air for for 6.3 seconds
Questions #5-8: Show graphically.
5. What is the maximum height of the ball?
6. How long after it is hit does the golf ball reach the maximum height?
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?
154 ft after 3.5 seconds, it is also this height at 2.75 seconds
8. At approximately what time is the ball 65 feet in the air? Explain.
At 0.737 seconds it reaches 65 feet in the air, and at approximately 5.5131 seconds it reached this height while falling.
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.
In 6 seconds he reaches the same height as the ball at 24 ft in the air.
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 hits the ground 1.25 seconds before Earls ball, but Glorias ball goes up a 100ft, while earls goes a 156.25ft.
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?
The ball would go 20ft higher in the same amount of time, but it would take longer to land on the ground
b. Write a function that describes the new path of the ball.
F(t)= -16t^2 + 100t + 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?
D= All real numbers
R= y < 176.25