Math (Trig)

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In 1893, the city of Chicago put on a World's Fair to celebrate the 400th anniversary of Columbus' trip to the Americas. The most spectacular at this fair was a huge Ferris Week built by an engineer named George Ferris. This remarkable structure had a diameter of 250 ft, was 30 ft wide and weighed about 4000 tons. There were 36 enclosed cars on the ride that seated a total of 1440 people, although as many as 2000 people could be accommodated through standing room. When a person was at the top of the ferris wheel, they were higher than a 20 story building.

Suppose that the diameter of this wheel is 250 ft and that the bottom of the wheel is 10 ft off the ground to assure that the cars do not strike the ground. Suppose also that when the car is in continuous motion it takes 60 seconds for it to make a complete revolution. As you watch a particular car travel around the wheel, you start a stopwatch and observe that the car reaches its highest point after 10 secongs.

a. draw a graph of the height of the car vs. the time since the stopwatch started

b. find an equation that models the height of the car above the ground versus time since you starter the stopwatch

c. how high is the car when the watch started? after 30 seconds? one minute? 45 seconds? 53 seconds?

d. what are the next two times that the car will be at its highest point?

e. when is the first time the car is 200 feet from the ground? what is the next time? the third time?