Timothy D. answered • 05/08/20

B.S. in Physics with 1 year Tutoring Experience

Kelvin N.

asked • 05/08/20Hi, I've been struggling with this question for weeks despite having adequate knowledge of the topic. If anyone could solve this for me and provide an explanation it would be greatly appreciated.

A ferris wheel has a diameter of 180m and the center of the wheel is 115m above ground. The wheel rotates continuously in a clock-wise direction at 1/26 rpm. Each visitor will get to enjoy 3 continuous rounds of the wheel.

At t = 0 (where t = time in minutes), Brandon gets into carriage A. The position of Brandon above the ground at the time t (in minutes) is given as y(A) (in meters).

You may use any of the following equations:

y(A) = a sin(bt + c) + d,

or y(A) = a cos(bt + c) + d

(a) Choose an equation that best describes the problem

(b) Find the amplitude, period, phase shift and vertical shift.

(c) Find the equation (a,b,c and d must have values)

(d) Determine the position of Brandon above the ground at t = 6 min

More

Timothy D. answered • 05/08/20

Tutor

4.9
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B.S. in Physics with 1 year Tutoring Experience

y(t)=a(sinbt+cj+d

because sine gives height, while cosine gives a horizontal distance, Y(t) represents height at time t

a=amplitude= half the diameter = 180/2 = 90 m = distance from midline to either max or min height

midline = 90+115=205

2bpi = period = 13/pi = 180/13 degrees = 13.85 degrees

1/26 rotations per minute = frequency = inverse of period =1/1/26=26 means 1 rotation every 26 minutes

sine curve repeats every 26 minutes, from t=0 to t=26. This is a very slow ferris wheel

the sine curve has a period of 2pi or 180 degrees if b=1

sinb(6.5)=1

6.5b = 90 degrees

b=90/6.5 = 18/1.3 = 13.85

c=phase shift = 16.128 degrees = 0.2815 radians = 0.0896 pi radians

Y(0)=115-90=25, since at t=0 ferris wheel is at minimum height.

90sin(0+c) =25 = 90sin(c)

sin(c)=25/90=5/18, c=16.128 degrees=0.2815 radians

d=vertical shift = 115m

y(t)=90(sin180t/13+16.128)+115

at t=6

Y(6)=90(sin6(180)/13+16.128+115

=90(sin83.077+16.128)+115

=90(sin99.205)+115

=0.9871(90)+115

=88.839 + 115 = 203.839 meters

at t=6.5 the ferris wheel is at its average height of 115+90=205 meters

at t=13 its at its maximum height = 115+180= 295

at t=0 it's at a minimum height of 115

a t=6, it should be slightly lower than its average height of 205

=

Y(26/4=6.5)=midline of the sine curve = 115+90= 205 meters= the height of the center of the ferris wheel

Y(6) should be a little less, <205

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Kelvin N.

Thank you so much!05/08/20