# Lets go Golfing!

## Whats going on?

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 a height modeled by the function f(t)=-16t^2+100t. Answers are rounded to the nearest hundredth.

## 1.) THE FUNCTION

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

(graphs title: height in feet of golf ball vs. time in seconds)

## 2.) What is our independent variable

The TIME (in seconds) is our independent variable. The height depends on the time, so the time is what is being changed to alter the height.

## What is our dependent variable?

The HEIGHT (in feet) is the dependent variable. The height DEPENDS on the time, and the height is what is being measures, so the height is the dependent variable.

D: 0 ≤ x ≤ 7

R: 0 ≤ y ≤ 157

## 4.) HOW LONG IS the golf ball in the air?

The ball is in the air for 6.25 seconds. We know this, because when graphed, the parabola starts at (0,0) and then rises to (3.13, 156.25) then falls back down to (6.25, 0). In our case the independent variable aka the x-axis represents the time, so if the ball hits the ground (which would be represented by a 0 in the y-value) and the x-value is 6.25, that means it took 6.25 seconds for the ball to reach back down to the ground.

## (graphs title: height in feet of golf ball vs. time in seconds)

When graphed, the parabola has a vertex of (3.13, 156.25). Since this graph opens downwards, this means the vertex is a MAXIMUM, which would also mean it is the highest point the ball will reach in the air. The 3.13 represents the number of seconds it takes for the ball to reach that point in the air, which is 156.25 feet (represented by the y-value, because the y-value represents height.)

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

As explained above, the x-value represents the seconds it takes for the ball to reach a certain value on the y-axis, which represents height in feet. At its vertex, or maximum point, the ball is at (3.13, 156.25). The time in seconds is the x-value so therefore it has taken the ball 3.13 seconds to reach it's maximum height of 156.25 feet.

## 7.) What is the height of the ball at 3.5 seconds?

When the x-value is 3.5 seconds (the seconds), the y-value (the height in feet) is 154 feet. It has also been at this same height at 2.7 seconds, before the ball reaches its maximum height.

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

At 7.4 seconds, the ball is at 65 feet in the air. The y-value is representing height, so we looked to see when the y-value was 65, and then looked to see what the x-value (which is the time in seconds) was for a y-value of 65 feet.

## Tweety Bird!

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.

## 9.) When will Tweety bird be the same height as your ball? What is that height?

Tweety Bird will be at the height of our ball after 6 seconds (which will be 24 feet).

f(t)=-16t²+100t

f(t)=4t

Since Tweety Bird is traveling 4ft per second, it would be 4t (time multiplied by 4).

## 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. Earl is represented by the green line. Gloria is represented by the red line. Gloria’s ball will hit the ground first. Her ball will hit 1.25 seconds before Earl’s. Gloria’s ball will reach a height of 100ft. That is around 57 feet less than Earl's ball.

## 11.) Suppose that 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?

-There is now a c in the function which means that there is now a y-intercept of 20. The ball that was teed off 20ft above the fairway will reach a greater height (it will be higher) than the original ball. Therefore, the y-intercept would be 20 feet higher, meaning it would intercept the y-axis at (0,20). The time it takes to reach the vertex will be the same, but the vertex will move up 20 units.

## A function to represent this situation

-f(t)=-16t²+100t+20

Title of graph: Height in feet vs Time in seconds

## Reasonable domain and range

domain: 0 ≤ x ≤ 3.13

range: 20 ≤ y ≤ 176.25