# Hot Air Balloons

### By: Sabarish and Amish

## 1) What best represents the situation with a function relating to variables?

**800 - 20x = y**

**y = altitude**

## 3) 5 minutes before the balloon was sighted, how high was it? Show graph and explain.

The graph below shows that the balloon was a 900 feet 5 minutes before it was sighted. The plot is the balloon at 900 feet which is the Y axis and it is -5 minutes which is 5 minutes before it was seen and the -5 is on the X axis.

## 4A) For the balloon to reach 20 feet altitude, how long will it take? Show a graph and explain.

The plot on the graph below shows that when the balloon will be at 20 feet altitude. As it shows in the graph, it will take exactly 39 minutes for the balloon to reach an altitude of 20 feet.

## 4B) For the balloon to land, how long does it take? Show a graph and explain.

In the graph below, the plot is showing the time it will take for the balloon to land. It will take 40 minutes for the balloon to land as you can see in the graph.

## 5A) The second ballon is sighted. It is descending at 20 feet per minute and is currently at 1200 feet. Write a function describing the event. How much longer will it take for the second balloon to land compared to the first balloon? Show the graph and explain the relationship between the 2 lines.

The functoin 1200-20x=y.

The graph below shows that it will take balloon two, 20 minutes longer than ballon one.

## 5B) How fast is the second balloon descending compared to the first?

As it shows in the graph above, they both descend at the same rate but they start at different altitudes so balloon 2 lands 20 minutes after the first balloon.

## 6A) A third balloon is spotted and it is descending at 30 feet per minute and it is currently at 800 feet. Write a function to represent this situation. When comparing the third balloon and the first balloon, how much longer does it take for the third balloon to land compared to the first balloon?

The function is 800-30x=y

According to the graph below, it takes -14 minutes longer to land.

## 6B) When they are descending, how do they compare? Show a graph and explain. Explain the relationship between the 2 lines.

As you can see with the graph above, they both start at the same altitude but descend at different rates.

## 7A) As soon as the first balloon is spotted, a 4th balloon is launched from the ground and is ascending at 30 feet per minute. Write the function that represents this situation. At what altitude will the first and fourth balloon be the same?

The function is 800-20x=0+30x

In the graph below it shows that balloons 1 and 4 will be at the same altitude at 16 minutes.

## 7B) What is that altitude? Show a graph and explain. What does this mean graphically?

As you can see in the graph above, balloons 1 and 4 will be at 480 feet.

This graph means that the first balloon is being released at the same time as the second balloon is spotted and descending. When they cross, it is called a point intersection.

## 8) In order for the 3rd balloon to reach the ground at the same time as the first balloon, what altitude would the third balloon have to start at? What is the equation of the line?

As it shows in the graph below, the altitude will have to be at 1200 for the 2 balloons to reach the ground at the same time.

The equation is 1200-30x=y