3The height that a seat on a ferris wheel reaches above the ground as the wheel

Question

3The height that a seat on a ferris wheel reaches above the ground as the wheel rotates may be found using the equation h 30+10cos(90r°). Where t is the number of minutes after starting and h is height in meters. a) What is the maximum height the seat reaches? b) What is the minimum height that a seat goes to? c) What is the distance between the seats? d) The graph of this is shown below What is the length of the period in minutes? If the operator wishes to speed up the wheel so that it now completes a cycle every three minutes, what changes have to be made to the equation? e)

Explanation / Answer

h = 30 + 10 cos(90t)

a)

Maximum height when cos(90t) = 1

Thus, h = 30 + 10(1) = 40 (possible at t=0,t=4 as cos 0, cos 360 = 1)

b)

Maximum height when cos(90t) = -1

Thus, h = 30 + 10(-1) = 20 (possible at t=2 as cos 180 = -1)

c)

distance between seats = Maximum height – Minimum height

= 40 -20 = 20

d)

Length of period in minutes

= time required to complete on revolution (360 degrees)

Thus, 90t = 360

Thus, t = 4 min

e)

If t =3 min, then

Xt = 360

X (3) = 360

X = 120

Thus, new equation will be

h = 30 + 10 cos(120t)

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