# Hot-Air Balloon

### Yutika Ineni and Anushya Alandur

At the West Texas Balloon Festival, a hot-air balloon is sighted at an altitude of 800 feet and appears to be descending and a steady rate of 20 feet per minute. Spectators are wondering how the altitude of the ballon is changing as time passes.

## Question 1

The function of the balloon is f(m) = 800 - 20m

## Question 3

Five minutes before the balloon was sighted, the balloon was 900 feet in the sky. The time sighted was -5 and the height was 900 feet. The coordinates are (-5,900). Refer to the graph above.

## Question 4

The balloon takes 39 minutes to reach an altitude of 20 feet. It takes 40 minutes to reach the ground at an elevation of 0 feet.

## Question 5

The function for balloon number 2 is f(m)= 1200 - 20m

It takes longer when the altitude is 1200 ft, than when it is 800 ft. It takes 20 more minutes to reach the ground for 1200 ft than 800 ft. It takes 40 minutes for the first balloon to land, and it takes 60 minutes for the second to land.

## Question 6

The function for balloon number 3 is f(m)= 800 -30m.

This balloon takes takes a smaller amount of time than the first 2 balloons since this balloon descends 30 ft/min, but the others descend 20 ft/min. This balloon takes 26 2/3 minutes to land while the other two land at 60 & 40 minutes.

## Question 7

The function for balloon number 4 is f(m)=30m.

At 16 min, the 1st and 4th balloons will be at the same altitude (480 ft). That is the point where both balloon intercept (16,480).

## Question 8

The 3rd balloon would have to start at an altitude of 1200 in order to reach the ground the same time as the 1st balloon. The equation is listed below