Hot-Air Balloon Project

By Kennedy, Katie, and Alaina




Here is the chart. Every 5 minutes, it descends 100 feet, and every 1 minute, it descends 20 feet.


It was 900 ft. above the ground. You can tell because if you go to x=-5, (which would be five minutes before seeing it because the x is minutes) the y, or feet=900. Also, our chart shows that it is at 900 feet if you need more evidence.


1200-20x. It takes 20 minutes longer, because they are descending at the same rate of 20 feet per minute, and the 2nd balloon is 400 feet higher to start, which translates to 20 minutes longer. Their descent paths are at the same steepness on the graph, because they have the same rate of change. The second one just starts at a higher height so it takes a little longer. The lines are parallel, and the both have a slope of -20.


800-30x. It takes the third balloon 26 and two thirds of a minutes, which is 13 and a third minutes shorter than the first balloon. The third finishes before the first. Because the third balloon descends 150% faster than the first, its line is much steeper. The first ballon's slope is -20, and the third's is -30, which is a relatively large difference.


30x. 1st and 4th are together at 16 minutes, 480 feet up in the air. Where the two lines intersect is where the two balloons meet. The fourth balloon's line goes up because its height does, while the other's goes down just as the balloon does. They meet at 16 minutes, and 480 feet, just like the labeled point says.


The third balloon would have to start at 1200 feet to end at the same time as the first, which makes sense since it goes 150% faster downwards and 1200 is 150% of 800. The equation of the line is 1200-30x.