Precalculus II Introductory Problems for Orientation to Communications

• describe any picture or graph you might have drawn to help you understand the situation,
• clearly communicate how you reasoned out your solution, showing the essential details, and
• ask questions about whatever you are not sure of.

Submit your responses by email and I will respond to them.

1.  Sketch a picture of a merry-go-round, as seen from above. The merry-go-round has a diameter of 40 feet.

At some specified time, a certain child is at a point directly to the East of the center of the merry-go-round, and right at the outer rim of the ride, which is moving at a constant rate of 1 revolution every 84 seconds.

• After how many seconds will the child be at the Northernmost point of the merry-go-round?
• After how many seconds will the child be at the Westmost and Southernmost points?

Use your picture to estimate the answers to the following. Don't use any knowledge you might have of trigonometry; just make good estimates.

• How far to the East or West, and how far to the North or South will the child be after 14 seconds have elapsed?
• How far after times 56, 35 and 70 seconds have elapsed since the original specified time?
• Through how many degrees will the child have rotated in each of these times?

2.  Sketch a picture of the following situation and use your picture to estimate answers to the questions asked. Don't use any knowledge of trigonometry, simply estimate from your picture.

A star defensive back sees a pass thrown into his zone. He quickly calculates that he must move to a position which is 7 yards down the field and 3 yards across the field, then with incredible speed, agility and timing he moves to that point and makes a spectacular play.

• At what angle, relative to the lines across the field (the 'gridlines'), does he decide to move?

Based on your previous answers, use your calculator to determine the following:

• What is the ratio of the distance moved down the field to the distance moved across the field?
• What is the ratio of the distance moved across the field to the total distance moved?
• What is the ratio of the distance moved down the field to the total distance moved?

Using these ratios, answer the following:

• If the player had moved `dist yards along the same line, how far would he have moved up the field and how far across?

3.  Imagine a Christmas tree on which there are 1000 lights, 500 of which are initially red and 500 of which are initially green. At the end of 1 minute, 15% of the red lights suddenly turn green and 10% of the green lights suddenly turn red.

• How many red and how many green lights are there at this time?
• If the same thing happens after a second minute has elapsed, then how many red and how many green lights are there now?
• Answer the same question for a third and a fourth minute.
• Sketch and describe a graph of the number of red lights vs. the number of minutes.
• How many red lights to you think there will be after 100 minutes?

4.  Sketch a straight line across a piece of paper, and sketch a point about an inch away from the straight line. Label the line D and the point f.

• Make a point halfway between the line D and the point f, and label it v.
• Now locate a point which is 2 inches from D and 2 inches from f.
• Repeat for a point 3 inches from both D and f.
• Repeat for points at various equal distances from D and f.
• If you could sketch all such points (you can't because there is an infinite number of them), what would the resulting line or curve (as the case may be) look like?