Ferris Wheel Math Question

Question

You are on a new concept Ferris wheel that is run as a hotel room. The center of the wheel is 10m above the ground. The diameter of the wheel is 6m. The ride lasts for 10 hours from start to the end. If the ride starts from the bottom of the wheel at 4PM, how high are you from the ground at 11PM? Round your answer to the nearest whole number.

Answer 1

amplitude = A = 6 meters

B = 2pi/period = 2pi/10= pi/5

D = midline = 10 + 6 = 16 meters= average height

C= phase shift =pi/5+pi/2 = 7pi/2

h(t) = AsinB(t - C) + D

h(t) = 6sin[(pi/5)(t)] +16

h(0) = 10 = 6sin[(pi/5)(0-pi/5-pi/2)]+16 which is 4pm

7 hours later at 11pm

h(7) = 6sin[(pi/5)(7-7pi/2)] +10

= 6sin(7pi/5 -7pi/2) +16

= 6sin[-2.1pi] +16

=6sin-6.6 +16 in radians

=6sin-378+ 16 in degrees

= 6sin-18 +16

=-6sin18+16

=14.15 meters high

=about meters high

10 hours later it's back to 10 m at 2 am