Hot-Air Balloon Graphs

Hot-Air Balloon GRAPHS

Use this graph throughout the Hot Air Balloon activity. Keep it neat and in a safe place.

Note: The y-axis needs to have a maximum of 1400 feet.

The x-axis needs a maximum of 70 minutes.


Hot-Air Balloon – Balloon-1

At the Boise, Idaho Balloon Festival, hot-air Balloon-1 is sighted at an altitude of 900 feet and appears to be descending at a steady rate of 20 feet per minute. Spectators are wondering how the altitude of the balloon is changing as time passes.

1. Make a table of values to show the balloon’s altitude every 5 minutes beginning
5 minutes before the balloon was sighted until the balloon lands.

Balloon-1 Altitude

Time, T
(Minutes) / Altitude
(Height, H, in feet)
-5

2. Graph the values from the table you completed in #1.
Be sure to include a title, labels, a consistent scale and appropriate intervals.

3. What was the height of Balloon-1 five minutes before it was sighted?


4. How did you determine the height of Balloon-1 five minutes before it was sighted?

5. How long does it take Balloon-1 to reach the ground?

6. What is the rate of the balloon’s descent?

7. What is the height of Balloon-1 at 23 minutes after being sighted?

Show your work using words, numbers and/or diagrams.

8. What is the height of the Balloon-1 eight minutes after being sighted?

Show your work using words, numbers and/or diagrams.

9. Write in words the height of Balloon-1 at t minutes after being sighted?

10. Write an equation to find the height (h1) of Balloon-1 at t minutes after being sighted?

(Be sure to graph your equation on the coordinate plane. J)

11. How do the numbers in your equation relate to the movement of the hot air balloon?
Be specific.

12. Determine how long it takes the balloon to reach an altitude of 20 feet?

Show your work using your equation from #10.


Hot-Air Balloon – Balloon-2

13. A second balloon, Balloon-2, is first sighted at an altitude of 1200 feet (treat the 1st sighting as t = 0) and is descending at a steady rate of 20 feet per minute.

What was the height of Balloon-2 five minutes before it was sighted?

Show your work using words, numbers and/or diagrams.

14. Make a table of values to show the altitude for Balloon-2 every 5 minutes beginning at
5 minutes before the balloon was sighted until the balloon lands.

Balloon-2 Altitude

Time
(Minutes) / Altitude
(Height in feet)
-5

15. Graph the values from the table you completed in #14 for Balloon-2.

(Use the same Cartesian coordinate plane you used to graph the data for Balloon-1).

16. How long does it take Balloon-2 to reach the ground?

17. What is the rate of the balloon’s descent?

18. What is the height of Balloon-2 at 23 minutes after being sighted?

Show your work using words, numbers and/or diagrams.

19. What is the height of Balloon-2 at 8 minutes after being sighted?

Show your work using words, numbers and/or diagrams.


20. How does the descent and landing time of Balloon-2 compare with that of Balloon-1?

21. What does this mean graphically?

22. Write an equation to find the height (h2) of Balloon-2 at t minutes after being sighted?

(Be sure to graph your equation on the coordinate plane.)

23. How do the numbers in your equation relate to the movement of hot air Balloon-2?
Be specific.

24. Determine how long it takes Balloon-2 to reach an altitude of 20 feet?

Show your work using your equation from #22.


Hot-Air Balloon – Balloon-3

25. A third balloon, Balloon-3, is first sighted at an altitude of 900 feet but is descending at 30 feet per minute.

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

Balloon-3 Altitude

Time
(Minutes) / Altitude
(Height in feet)

26. Graph the values from the table you completed in #25 for Balloon-3.

(Use the same coordinate plane you used for Balloon-1 and Balloon-2).

27. What was the height of Balloon33 just 5 minutes before it was sighted?

28.How long does it take Balloon-3 to reach the ground?

29. What is the rate of the balloon’s descent? _

30. What is the height of Balloon-3 at 23 minutes after being sighted?

Show your work using words, numbers and/or diagrams.

31. What is the height of Balloon-3 at 8 minutes after being sighted?

Show your work using words, numbers and/or diagrams.

32. How does the descent and landing time of Balloon-3 compare with that of Balloon-1?

33. What does this mean graphically?

34. Write an equation to find the height (h3) of the balloon at t minutes after being sighted?

(Be sure to graph your equation on the coordinate plane.)

35. How do the numbers in your equation relate to the movement of hot air Balloon-3?
Be specific.

36. Determine how long it takes Balloon-3 to reach an altitude of 20 feet?

Show your work using your equation from #34.


Hot-Air Balloon – Balloons-4 & -5

37. At the instant the first balloon is sighted, a fourth balloon, Balloon-4, is launched from the ground, rising at a rate of 30 feet per minute.

Make a table of values to show the balloon’s altitude every 5 minutes beginning at the time the balloon was first sighted until the balloon reaches an altitude greater than 1000 feet.

Balloon-4 Altitude

Time
(Minutes) / Altitude
(Height in feet)

38. Graph the values from the table you completed in #37 for Balloon-4.

(Use the same coordinate plane you used for Balloon-1, Balloon-2, and Balloon-3).


39. What is the rate of ascent for Balloon-4?

40. What is the height of Balloon-4 at 23 minutes after being sighted?

Show your work using words, numbers and/or diagrams.

41. Write an equation to find the height (h4) of Balloon-4 at t minutes after being sighted?

(Be sure to graph your equation on the coordinate plane.)

42. How do the numbers in your equation relate to the movement of hot air Balloon-4?
Be specific.


43. Determine how long it takes Balloon-4 to reach an altitude of 20 feet?

Show your work using your equation from #41.

44. When will Balloon-1 and Balloon-4 be at the same altitude?

Show your work using words, numbers or diagrams.

a. What is that altitude?

b. What does this mean graphically?

46. The equation of a Balloon-5 is h5 = 700 – 20t.

How would the movement of this balloon compare to that of Balloon-1?

HOT AIR BALLOONS

MULTIPLE CHOICE PRACTICE PROBLEMS

47. The scatter plot shows the number of job offers and grade point averages for the students in an economics class.

Which describes the line of best fit for the given data points?

A. A horizontal line

B. A vertical line

C. A line with a negative slope

D. A line with a positive slope

48. The graph shows how many blossoms are not infected with fungus after being sprayed.

Which is the best prediction of how many uninfected blossoms you would expect to find on day 12?

A. 4

B. 6

C. 8

D. 10

Student: Ch. 5 “Hot Air Balloons” 4/23/08 Page 13 of 14