trigonomery

Question

Once everybody board Ferris wheel makes one complete revolution every 2.4 minutes. Wheel has diameter 150 feet clears ground 4 feet. Assume new riders board low point cycle.

Answer 1

1 revolution every 2.4 minutes

wheel diameter = 150 feet

passengers board the Ferris wheel at 4 feet about ground

f(t) = Asin(t(B+C))+D

A= amplitude = (max-min)/2 = 154-4)/2 = 150/2 = 75 feet

B = frequency, period=2pi/B= 2.4, B =2pi/2.4= pi/1.2

C = phase shift

D = mid-line = average height = (154+4)/2 = 158/2 = 79 feet high

f(0) = 4 feet = 75sin(0+C)+79 sinC=-1, C =arcsin-1= -pi/2

f(t) = 75sin(t(B -pi/2) +79

f(t) = 75sin(t(pi/1.2 - p/2)) + 79

= 75sin((pi/3)t) +79

B depends on the 1 revolution per 2.4 minutes, period = 2.4 minutes. B=2pi/2.4 =pi/1.2