Suppose that you are on a Ferris wheel which turns in a coun

Suppose that you are on a Ferris wheel, which turns in a counter-clockwise direction, that your height h(t), in meters above the ground at time, t, in minutes is given by h(t) = -20 cos(pi/5t) + 25 a. How high above the ground are you at time t = 0? b. What is the radius of the wheel? C. How long does one revolution take? d. What is the angular velocity? e. What is your linear velocity?

Solution

a)
When t =0,
h = -20cos(0) + 25
h = -20 + 25
h = 5

When t = 0, you are 5 meters above ground

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b)
Max = 20 + 25 = 45
Min = -20 + 25 = 5

Difference = 45 - 5 = 40 = diameetr

So, radius of the wheel = 40/2 = 20 meters

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c)
Period = 2pi/B

Here B = thing multiplied to \'t\'

Period = 2pi / (pi/5)

= 2pi * 5/pi

= 10

So, period = 10 minutes

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d) angular velocity :
10 minutes to complete 1 revolution
10 min to complete 2pi radians

So, ang vel = 2pi/10

= pi/5 radian per minute

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e)
Linear vel :
Linear vel = angular vel * radius

Linear vel = pi/5 * 20

Linear vel = 4pi meter per minute