For today's warmup, we looked at problem #1 with the skateboarder and the merry-go-round. The skater actually moves in a straight line, which happens to also be the tangent line to the circle at that point.

We defined the tangent line to be a line that crosses the circle at one point, and the tangent is perpendicular to the radius at that point.

To test this at home, you can tie an object (remote control, stuffed animal, a balled up sheet of paper, etc.) with string. Swing the string and object around yourself in a circle. Then let go of the string, and watch the object fly. You should notice that the object continues in a straight line (except that it sinks to the ground). This straight line is tangent to the circle.

Problem #2 asked us to apply this to our Ferris wheel problem. The diagram illustrates the path the diver takes after being released from the 4 o'clock position. Notice the initial path is the tangent to the circle, but then gravity causes the diver to fall.

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