How long does it take for the wheel to complete a full circle

Question

Andrew is watching a Ferris wheel rotate at constant speed. There are many lights around the Ferris wheel, and Andrew watches a green light closely. The height of the green light after t seconds is given by H(t) = 10 sin(π/50(t-25)) + 12 metres.How long does it take for the wheel to complete a full circle?

Answer 1

period of a sinusoidal function = 2pi/|B|

B= pi/50

2pi/B

=2pi/(pi/50)

= 2pi(50/pi)

= 100 seconds

= 1 2/3 minutes

= 1 minute 40 seconds

the ferris wheel has a diameter of 20 meters

It's circumference =2pir = pi(20) = 20pi

a seat on the wheel moves 20 pi meters every 100 seconds

pi meters every 5 seconds

=about 1.4 mph