# Hot Airballoon

### Math Project By Ajay Amit and Ethan Duong

## 1.

Since the balloon was dropped at 800 feet and is descending at a rate of 20 feet per minute the function is Y=800-20x. The height of the balloon is 800 feet and it is descending 20 feet every minute. X is the amount of time and Y is the height of the balloon.

## 2.

This is the graph and table that shows the altitude of the balloon every 5 minutes.

## 3.

The balloon was at 900 feet 5 minutes before it was first sighted. The function would be Y=800-(x-5)20. This picture shows where the balloon was before appearing. X is the amount of time and Y is the height of the balloon.

## 4.

The comparison is that it will take 39 minutes for the balloon to reach 20 feet and it will take 40 minutes for the balloon to reach the ground.

## 5.

Since the balloon started descending at 1200 feet and at a rate of 20 feet per minute the function will be Y=1200-20x. Since this balloon appeared higher than the first balloon and is descending at the same rate. The second balloon will arrive 20 minutes after the first balloon. Both balloons are descending at the same rate, but since the balloons were dropped from different heights the amount of time it takes for them to land are different. X is the amount of time and Y is the height of the balloon.

## 6.

This new balloon will arrive 14 minutes earlier than the first balloon since it was dropped at the same height (800 feet) but this one is descending at the faster rate of 30 feet per minute. The function that will go with this new balloon would be Y=800-30x. The relationship is that the new line is much steeper since it is descending faster. X is the amount of time and Y is the height of the balloon.

## 7.

This balloon is rising at a rate of 30 feet per minute which means it's function will be Y=30x. This balloon and the first balloon will meet at the altitude of 460 feet. This will happen in 16 minutes. Graphically this will mean when the two lines cross.

## 8.

In order for balloon three to meet up with balloon one it will need to start it's descent at 1200 feet. This has to happen since balloon 3 descends at a rate of 30 feet per minute while balloon 1 descends at a rate of 20 feet per minute. The equation that would go with the third balloon will be Y=1200-30x.