# The Hot Air Ballon

### By: Varsha K., Sai H., Evan B., Tristen S.

## A balloon is descending at 20 feet per minute. It stated at 800 feet write a function comparing the variables.

The X-Variable is minutes and the Y-Variable is height.

A function to describe this would be f(x)=800-20x because it starts at 800 feet and descends at a rate of 20 feet per miniute.

## How high was the balloon 5 minutes before it was sighted.

Since the balloon falls 100 feet per 5 minutes. 5 minute before it was sighted you would add 100 feet and it would equal to 900 feet.It changes by 100 units either way. This is the graph of the first balloon and it shows that at 5 minutes before it was at 900 feet.

## How long would it take the balloon to be at an altitude of 20 feet?Land?

It would take the balloon 39 feet to be at an altitude of 20 feet because it descends at a steady rate and it took 40 minutes to land. At 40 minutes the balloon is at 0 feet, while that means 39 would equal 20 due to the rate of change. This graph shows the first balloons decent and its height at 39 minutes or an altitude of 20 feet.

## What would happen if a second balloon was sighted at 1200 feet and is falling at 20 feet per minute.How long does it take to land?How does it compare to the first balloon?

The balloons function would be f(X)=1200-20x because it starts at 1200 feet and defends at a rate of 20 feet per minute. It would take 60 minutes for this balloon to land 20 more minutes than the first balloon. The balloons rate of change is the same but the starting altitude is different, which means the graph would be tessellated or moved up by 400 units. Parallel to the first.

## A third balloon is sighted at 800 feet and falling at 30 feet per minute.How much time does it take to land compared to balloon one?How do the descents compare?

The function would be f(X)=800-30x because it is sighted at 800 feet and descends at 30 feet per minute.The balloon takes about 27 minutes to land 13 minutes quicker than the first. The balloons start at the same point but the third one has a much quicker decent and will have a steeper graph while the first is more spread out over a long distance.

## A fourth ballon is launched from the ground at the same time the first balloon is sighted and its rising at 30 feet per minute. When will the balloons be at the same height?What is this altitude?What does the graph show?

The balloons function would be f(x)=30x because it rises constantly at a rate of 30 feet per minute. The balloon will be at the same height in 16 minutes.They would be at an altitude of 480 feet. The graph will look like an X because one is rising and one is descending and the intercept will be when they are at the same height.

## What height must the third balloon begin its decent to land at the same time as the first.

The third balloon must start at 1200 feet to land at the same time as the first. You would figure this out by multiplying the time it took the first balloon to land(40 minutes) and the third balloons decent(30 feet per second) and you would get the altitude(1200 feet).The equation then would be 1200-30x.The graphs would start at different points and would cross at 0 because they land at the same place.