URGENT QUESTION

Question

Bert is on a Ferris wheel. The radius of the Ferris wheel is 6 metres. Its axle is 7 metres above the ground. It takes 100 seconds to complete one full revolution. Bert enters the Ferris wheel at its lowest height. The ride starts at 0 seconds.

Work or explanation must be provided for full marks. Answers involving radians will result in a mark of zero.

a) Sketch a height vs time graph of ONE cycle of Bert’s motion on the ride.

Show at least 5 KEY POINTS and label them on your graph.

b.) Determine an equation of the sinusoidal function h(t) to represent Bert’s journey, where h represents the height of the Ferris Wheel and t represents the time in seconds. Choose the MOST appropriate sinusoidal function based on the information provided.

Answer 1

radius = 6 meters

7 meters above ground

100 seconds for one revolution

starts at zero seconds

y = AsinB(t-C) +D

A = Amplitude = (max-min)/w = (13-7)/2 = 3

D = (13+7)/2 = 10

2pi/B = period= 100

B = 2pi/100 = pi/50

C = phase shift, at time t= 0 y=7 and 3sin((pi/50)(0-C))+10=7

sin( -Cpi/50) = -1

-Cpi/50 = pi/3

-Cpi = 50pi/3

C = -50/3

h(t) = 3sin[(pi/50)(t+50/3)]+10

h(12.5) = 3sin(12.5pi/50+50/3) + 10

= 3sin(pi/4+50/3)+10

= 3(.3)+10= 10.9

h(0) = 7 (7,0)

h(50) =13 (13,50)

h(25) = 10 (10,25)

h(75) = 10 (10,75)

h(12.5) = 10.9 (12.5,10.9)