Relaxing at the Mansion

Congratulations, you sunk the boat and the torpedo! The threat to Staffa island has been eliminated for now and you deserve some rest and relaxation. While enjoying your mansion, you decided to watch a few Man vs. Wild episodes with Bear Grylls. In one of the episodes, he determined the height of a cliff by dropping a rock. He said that a rock falls about 50 feet for every second. But that doesn't seem right. The acceleration of the rock (at 32 feet per second per second) is a constant, but the velocity increases as it falls which means the distance per second increases over time. You decide to figure out how far a rock falls after each second up to five seconds. This will be a useful table of numbers to keep in your head while exploring.

Hints:

• First make a graph of the velocity vs. time, with velocity (in feet per second) on the y-axis and time in seconds on the x-axis
• To get the distance, you need to multiply the velocity (ft/s) times the time (s) which will give you the distance (ft) traveled during that time.
• Unfortunately, the velocity is changing over time, so which number should you use? Fortunately, your graph has the velocity at each time and the distance traveled is actually the area under the line because the area is also the velocity (y-axis) times the time (x-axis).