Hot Air Balloon

Jessica, Jack, and Hiro

Question #1

What function relating the variables best describes this situation?



f(x)=800-20x

Question #2

Make a table of values and a graph to show the balloon's altitude every 5 minutes beginning at 5 minutes before the balloon was sighted until the balloon lands.


Graph can be found below.



Question #3

How high was the balloon 5 minutes before it was sighted? Show graph and explain.



900 ft in the air, 100 ft higher than the 1st balloon.

Because it decends at a rate of 100 ft every 5 minutes, it would be at 900 ft 5 minutes before it was at 800 ft.


Question #4

How long does it take the balloon to reach an altitude of 20 ft? How long does it take the balloon to land? Show graph and explain.



It takes 40 minutes to land, and 39 minutes to be 20 ft in the air.

Because it decends at a rate of 20ft every minute (100ft every 5 minutes). 800 divide by 100 times 5 =40. since it desends 20 ft evey minuet, 40 minus 1 = 39, 20ft above ground.


Question #5

A second balloon is first sighted at an altitude of 1200 feet but is descending at 20 feet per minute. Write the function that represents this situation. How much longer does it take for the second balloon to land compared with that of the first balloon? How does the descent of the balloons compare. Show the graph. Explain the relationship between the two lines.


f(x)=1200-20x. It takes ! hour which 20 minutes longer than first ballon.

since it decends at same rate, it's parallel- never touching each other.




Question #6

A third balloon is first sighted at an altitude of 800 feet but is descending at 30 feet per minute. Write the function that represents this situation. How much longer does it take for the third balloon to land compared to the first balloon? How does the descent of the balloons compare? Show the graph. Explain the relationship between the two lines.


f(x)=800-30x. 26 1/3 minuets to land and 13 2/3 minutes longer .

It intersects at y-axis because it's not same rate. third ballon desends faster, rate of -30ft every minutes.

Question #7

At the instant the 1st balloon is sighted, a 4th balloon is launched from the ground rising at a rate of 30 feet per minute. Write the function that represents the situation. When will the 1st and 4th balloon be at the same altitude? What is that altitude? Shoe the graph. What does this mean graphically?



f(x)=30x


They'll be at the same altitude at 16 minutes, 480 feet.


Question #8

At what altitude would the 3rd balloon have to begin its descent in order to reach the ground at the same time as the 1st balloon? What is the equation of the line?


An altitude of 1210 feet.


y=1210-30x