Please Solve it In an attempt at exposing Data to yet another human form of ente

Question

Please Solve it

In an attempt at exposing Data to yet another human form of entertainment, Geordi wanted to take Data on a Ferris wheel ride. Data was puzzled as to how sitting in a "gondola" that rotates in a circular fashion could at all be entertaining; and so he asked Geordi for more details on the peculiar ride. Geordi, knowing Data so well, said the following: "Let H be a height function in feet of time, t, in minutes. The gondola you will be sitting in has a path that can be described by H(t) = -50 cos( pi /2t) + 50." Immediately Data was convinced that he should try the strange form of entertainment. Explain why the equation does a good job representing Data's height on the Ferris wheel as a function of time. At what time, t, will Data's gondola reach the top of the wheel? At what time, t, docs the wheel complete one cycle? Use complete sentences.

Explanation / Answer

I am not pretty sure why Data was immediately convinced that he should try the strange form of the entertainment.

Maybe it was because the slope at the top would be zero and hence he would like it?!

Anyway,

Ferris wheel moves in a circle. Hence the equation which is nothing but a sine wave in polar form does a good job of representing Data's height as a function of time.

For maximum height,

cos( .. ) = -1

pi* t /2 = (2n + 1) pi

t = 2(2n +1) minutes

The first time would be at t = 2 minutes

initially, H = 0

when pi*t/2 = 2pi, H is again 0

hence t = 4 minutes

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