# Hot Air Balloon

### By: Prayusha P., Jade R., and Vishal V.

## I LOVE MATH!!!!!!!!!!!!!

## Question 1

The function that relates to the variables that best describes the situation was f(x)=800 -20x because the situation explained that the balloon was found at the altitude of 800. Also, the balloon was descending at a rate of 20 feet per minute.

## Question 5 The function of the 2nd balloon is f(x) = 1200 - 20x where x is the number of minutes. The 2nd balloon takes 20 more minutes to land then the first balloon.We know this because 1200 is 400 more than 800 which is the altitude of the first balloon when first spotted.So with this 400 we divide it by 20 because that is the steady rate of decrease of 20. It will leave you with 20 minutes and that shows how the first balloon and second balloon will be 20 minute different. The relationship between the 1st and 2nd balloons is that the lines of both have the same slope and the 2nd balloon will always be 400 ft higher than the 1st balloon until the 2nd balloon has been going down longer than 40 minutes. | ## Question 4 It will take the balloon 39 minutes to reach 20 ft above the ground and it takes the balloon 40 minutes to land. We got this because the balloon descends at a steady rate of 20 feet per minute.We have to divide 800 by 20 to get 40 minutes if you want to know when the balloon reaches the ground..To find out how long it would take for the balloon to reach 20 ft above the ground we subtract 40 minutes from 1 minute to get 39 minutes. | ## Question 3 The altitude of the balloon 5 minutes before it was spotted was 900 feet. We got that answer because the function was f(x)=800-20x. Also the balloon was going down at a rate of 20 feet per minute. So -5*-20 = 100. So we add 100 to 800. So we got 900 feet. |

## Question 5

The function of the 2nd balloon is f(x) = 1200 - 20x where x is the number of minutes. The 2nd balloon takes 20 more minutes to land then the first balloon.We know this because 1200 is 400 more than 800 which is the altitude of the first balloon when first spotted.So with this 400 we divide it by 20 because that is the steady rate of decrease of 20. It will leave you with 20 minutes and that shows how the first balloon and second balloon will be 20 minute different. The relationship between the 1st and 2nd balloons is that the lines of both have the same slope and the 2nd balloon will always be 400 ft higher than the 1st balloon until the 2nd balloon has been going down longer than 40 minutes.

## Question 4

It will take the balloon 39 minutes to reach 20 ft above the ground and it takes the balloon 40 minutes to land. We got this because the balloon descends at a steady rate of 20 feet per minute.We have to divide 800 by 20 to get 40 minutes if you want to know when the balloon reaches the ground..To find out how long it would take for the balloon to reach 20 ft above the ground we subtract 40 minutes from 1 minute to get 39 minutes.

## question 2 The table and graph shows that the 1st balloon's altitude is decreasing at a steady rate of 20 ft every 5 minutes starting with 5 minutes before the balloon was first sighted and continues until it reaches the ground. | ## question 2 (cont.) | ## question 2 (cont.) |

## Question 2 Graph | ## Question 6 The function of the 3rd balloon is f(x) = 800 - 30x. This means that it will take the 1st balloon exactly 13 minutes and 20 seconds longer to land than the 3rd balloon.We know this because in the graph, we subtracted the x-intercept of the 1st balloon and the x-intercept of the 3rd balloon and we got 13 minutes and 20 seconds. The x- intercept is the point of when the line crosses the x- axis.The line of the 3rd balloon will be steeper than the line of the 1st balloon, since the 3rd balloon descends at a faster pace of 30 feet per second rather than the 1st balloon which descends at 20 feet per second and they both are at the same altitude which 800 ft. | ## Question 7 The function of the 3rd balloon is f(x)= 30x where x is the number of minutes. The 1st and 4th balloons will be at the same altitude after 16 minutes and the altitude will be 480 ft and the point of intersection is (16,480).This shows the point where both balloons will be at the same altitude at the same time. |

## Question 6

The function of the 3rd balloon is f(x) = 800 - 30x. This means that it will take the 1st balloon exactly 13 minutes and 20 seconds longer to land than the 3rd balloon.We know this because in the graph, we subtracted the x-intercept of the 1st balloon and the x-intercept of the 3rd balloon and we got 13 minutes and 20 seconds. The x- intercept is the point of when the line crosses the x- axis.The line of the 3rd balloon will be steeper than the line of the 1st balloon, since the 3rd balloon descends at a faster pace of 30 feet per second rather than the 1st balloon which descends at 20 feet per second and they both are at the same altitude which 800 ft.

## Question 7

The function of the 3rd balloon is f(x)= 30x where x is the number of minutes. The 1st and 4th balloons will be at the same altitude after 16 minutes and the altitude will be 480 ft and the point of intersection is (16,480).This shows the point where both balloons will be at the same altitude at the same time.

## Question 8

For the 3rd balloon would have to begin its descent at 1200 ft to end at the same time as the 1st balloon. We know this because the speed that the 3rd balloon descends is 2/3 faster than the 1st balloon. So to be even with the 1st balloon, the altitude of the 3rd balloon must also be 2/3 larger which is 1200 ft. The equation of the line for this is y = 1200 - 30x.