# Golfing Project

### By: Katie Austin, Ashley Miznazi, Steve Koshy

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

;)

## 1) GRAPH f(t)=-16t²+100t

This is the graph

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?

IV: Time in seconds

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?

domain: 0 ≤ x ≤ 6.25

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?

The golf ball is in the air 6.25 seconds. (You can tell because after this, the golf ball's y value, or height, would go underground.) 0 is the lowest it can go, and it hits 0 at 6.25 seconds.

## 5) What is the maximum height of the ball?

The maximum height of the ball 156.25 ft. When you solve for the MAX in the calculator, it gives you that y value for the vertex. The y value is height.

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

Max: 3.13 seconds rounded, or 3.125 seconds to be exact.

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?

154 ft, and yes. 2.75 seconds is another time it is at the same height. If you plug 154 into X cal that's the other value it gives you.

## 8) At approximately what time is the ball 65 feet in the air? Explain.

About 0.74 seconds, or just 1 if you want to be simple. That it what you get if you plug 65 in for the y value. Also, at 5.51 seconds, it is at 65 feet again.
please ignore the red dot on the side, but this is the other time

## 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.

They meet at 6 seconds, 24 feet. Also at takeoff, 0 feet and 0 seconds. That's when they intersect, so it's for sure.

## 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.

The blue is Earl's original swing. The blue is after he is elevated in the tree by 20 feet. The vertex is 20 feet higher.

## 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)