Hot Air Balloon Project
Rohil V / John C / Het D
At the West Texas Balloon Festival, a hot-air balloon is sighted at an altitude of 800 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.
This function best describes the situation:
f(x) = 800 - 20x
f(x) = 800 - 20x
The balloon was 900 feet in the air 5 minutes before it was sighted because if it decreases if x is positive, it will increase if x is negative. (see graph above)
It takes the balloon 39 minutes to reach an altitude of 20 feet because for every 1 minute, it decreases 20 feet. It takes the balloon 40 minutes to land. (see graph below)
The function that describes the second balloon is: f(x) = 1200 - 20x. It takes 60 minutes for the second balloon to land, compared to 40 minutes for the first balloon to land. The second balloon decreases at the same rate as the first balloon, but it starts 400 feet higher, at 1200 feet.
The function for the 3rd balloon is: f(x) = 800 - 30x. It takes 26 minutes and 40 seconds to land rather than 40 minutes (first balloon). It starts at the same height as the second balloon and 400 feet higher than the first balloon, but decreases at a faster rate than both of them.
The function of the fourth balloon is f(x) = 30x. The fourth balloon and first balloon will meet after 16 minutes, at 480 feet. This is because if 30x = 800 - 20x, then x becomes 16. Then if the fourth balloon increases at 30 feet every minute, then 30*16 = 480.
The 3rd balloon would have to begin its descent at 1200 ft in order to reach the ground at the same time as the 1st balloon. The equation of the line is: y = 30x + 1200