# Hot Air Balloon Project

### By Camrin W. and Noah N.

## Question 1

At the West Texas Balloon Festival, a hot-air balloon is sighted at an altitude of 800 feet and appears to be descending at a steady rate of 20 feet per minute. Spectators are wondering how the altitude of the balloon is changing as time passes.

1. What function relating the variables best describes this situation?

F(x)=800-20x

## Question 2

**2. Make a table of values and a graph to show the balloon’s altitude every 5 minutes beginning at 5 minutes before the balloon was sighted until the balloon lands.**

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## Question 3

How high was the balloon 5 minutes before it was sighted? Show graph and explain.

900 ft in the air because 5 minutes before it was sighted would be 900 ft since it was descending.

## Question 4

4. How long does it take the balloon to reach an altitude of 20 feet? How long does it take the balloon to land? Show graph and explain. 39 minutes for it to reach 20 feet. It will take 40 minutes for the balloon to land.

## Question 5

5. A second balloon is first sighted at an altitude of 1200 feet but is descending at 20 feet per minute. Write the function that represents this situation. How much longer does it take for the second balloon to land compared with that of the first balloon? How does the descent of the balloons compare? Show the graph. Explain the relationship between the two lines. F(x)=1200-20x It will take the second balloon 20 minutes longer than the first balloon to land. The descent rates are the same at 20 feet per minute, but the second balloon starts descending 400 feet higher. The blue line on the graph

is balloon one and the red line is second balloon.## Question 6

6. A third balloon is first sighted at an altitude of 800 feet but is descending at 30 feet per minute. Write the function that represents this situation. How much longer does it take for the third balloon to land compared with that of the first balloon? How does the descent of the balloons compare? Show the graph. Explain the relationship between the two lines.

f(x)800-30x The third balloon will land about 16 minutes earlier than the first balloon since it is descending at a faster rate (30 feet /minute) Both balloons start at 800 feet, but the third balloon descends quicker at a rate of 30 feet per minute and the first descends at 20 feet per minute. The blue line is the third balloon and the first balloon is the red line. The blue line lands quicker than the red line.## Question 7

7. At the instant the first balloon is sighted, a fourth balloon is launched from the ground rising at a rate of 30 feet per minute. Write the function that represents this situation. When will the first and fourth balloon be at the same altitude? What is that altitude? Show the graph. What does this mean graphically? F(x)=30x

16 minutes. They will equal and it would be at 480 feet

This will be where they meet up and pass each other.

## Question 8

8. At what altitude would the 3rd balloon have to begin its descent in order to reach the ground at the same time as the 1st balloon? What is the equation of the line?

1200ft in the air for it to reach the same time. 1200-30x=800-20x