Suppose that the height above ground of a person sitting on a Ferris wheel is described by the following.

Question

Suppose that the height above ground of a person sitting on a Ferris wheel is described by the following.

h(t)= 17.6-15.5cos(2pi/5)t

In this equation, h(t)

 is the height above ground (in meters) and t

 is the time (in minutes). The ride begins at t=0

 minutes.During the first 5

 minutes of the ride, when will the person be 12

 meters above the ground?Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a minute.

Answer 1

Hi Martha! So this question can be done in two ways, one being much simpler than the other. If you have a graphing calculator, you can plug 17.6 - 15.5cos(2pi/5)t into y1 and 12 into y2. Then before you graph it, you can change your window so that your Xmax is 5, as the problem specifies that it wants the times within the first 5 minutes. If you follow these steps, you should get the answers to be 0.96 seconds and 4.04 seconds.

The other way you could approach this problem is to solve it by setting 17.6 - 15.5cos(2pi/5)t = 12. You would first subtract 17.6 on both sides, then divide by -15.5 on both sides, then use inverse cosine on both sides and finally multiply by the reciprocal. The tricky part here is that inverse cosine has two answers in this case because cosine is positive in the first and fourth quadrant. So in this specific case you would get inversecosine of 0.3612903226) to have two answers which are 1.20114501 and 5.082040296. If you take these two numbers and multiply them by the reciprocal of 2pi/5 you will get the same answers as if you had used the graphing calculator: t=0.96 seconds and 4.04 seconds