# Hot Air Balloon!

## Question #1

A hot-air balloon was spotted at 800 ft. and was descending ate 20 ft. per minute. What is a function that shows the altitude as time passes?

y = 800-20x

Why? Because the starting altitude is 800 ft. and as the balloon descends or goes down, you have to subtract 20 ft. for each minute. (x)

## Question #2

A. Make a table that to show the altitude of the balloon every 5 minutes.

B. Make a graph showing the same information.

Why? Since the balloon is descending or falling, the blue line which is the balloon is also falling.

## Question #3

5 minutes before the balloon was sighted, or at -5 minutes, what was the height of the balloon?

900 ft.

Since they noticed it at 800 ft. and the balloon is moving at a rate of 100 ft. per 5 minutes, then at “-5” minutes (5 minutes before it was spotted and being charted) the altitude of the balloon was at 900 ft.

Why? As you can see, there is a little purple curser at about x = -5 and y = 900. What does this mean? x is how many minutes and y is how high the balloon is. So, 5 minutes before the balloon was sighted, the balloon was at 900 ft.

## Question #4

A. When will the balloon be 20 ft. off the ground?

39 minutes.

B. When will the balloon land?

40 minutes.

Why? Each minute the height of the balloon falls by 20 ft., so at 39 minutes, the balloon is only 20 ft. off the ground. IN one more minute, the balloon has landed.The purple curser on the graph shows this.

## Question #5

A. A new balloon, balloon 2, is sighted at 1200 ft. in the air and is falling at the same speed as balloon 1. What function shows this?

y =1200-20x.

B. How much longer will it take balloon 2 to land than balloon 1?

20 more minutes.

C. How does the falling of the balloons compare?

They fall at the same speed, but balloon 2 starts higher up, so it lands later.

Why? The red line (balloon 2) is falling at the exact same speed, but is further to the right meaning it is taking longer. How? Balloon 2 started higher up than balloon 1 so it took longer to fall.

## Question #6

A. Balloon 3 starts at 800 ft. like balloon 1, but is falling faster. It is falling at 30 ft. per minute. What is a function for this balloon?

y = 800-30x

B. How many more minutes does it take balloon 1 to land?

13 1/3 more minutes.

C. How do the two balloons compare?

Balloon 3 is falling or descending faster that balloon 1.

Why? Though their y intercept is equal,meaning they start falling at the same point, because the 3rd balloon in blue falls at 30 ft. per min. and the 1st balloon falls at 20 ft. per minute, the 3rd balloon landed about 13 1/3 minutes earlier.

## Question #7

A. At the same time balloon 1 starts falling, balloon 4 starts to rise. It rises at 30 ft. per minute. What function shows this?

800-20x = 30x

B. When will both of the balloons be next to each other or at the same height?

at (16,480) or 16 minutes and 480 ft. high.

C. What does it mean in the graph?

This means that the 4th balloon, the red, even though it is increasing and not decreasing like the 1st balloon, the blue, intersect at y at the exact same time. Also, they intersect at 16,480.

Why? Since balloon 4 is rising and balloon 1 is falling, they have to intersect or cross at some point. Where the two lines cross is where the balloons would cross.

## Question #8

Where would balloon 3 have to start in order for it and balloon 1 to reach the ground at the same time?