Question

A Group of students is tracking a friend, John, who is riding a Ferris wheel. They know that John reaches the Maximum height of 11 m at 10 seconds and then reaches the minimum height of 1 m at 55 seconds.

What is the period of the function and what does it represent in this situation?

Answer 1

Answer: Period = 90 seconds

The period represents how long it takes go from one max to the next max (ie peak to peak). It also represents going from min to min.

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Step-by-step explanation:

It reaches the max at 10 seconds, and then it reaches the min at 55 seconds. This is a timespan of 55-10 = 45 seconds. This is exactly half the period. It doubles to 2*45 = 90 seconds. This is the time period between any two points in time when you're at the max height (from one max to the next adjacent max).

So you're at the max height at 10 seconds, then min at 55 seconds, then the max again at 100 seconds. Note how 100-10 = 90.

The period of any trig function is basically telling us when the function or cycle repeats itself. Once we reach the peak again, the ride repeats itself from before.

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Notes:

• 90 seconds = 1 minute, 30 seconds = 1.5 minutes
• The actual heights listed (11 m and 1 m for the max and min respectively) do not play a role in determining the period. So the heights can be anything we want, and the period will stay at 90 seconds.