Homework: Modeling with Trig Functions (Section 6.5)

Question

A Ferris wheel is 35 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. How many minutes of the ride are spent higher than 30 meters above the ground?

Minutes:

Answer 1

5.824 minutes or

about 5 minutes and 50 seconds

the ferris wheel can be modeled with the equation of a circle

x^2 + y^2 = r^2

half the diameter = 17.5

when y> 11.5 meters, the ride > 30 meters above ground

29-17.5=11.5

30-1 = 29

30 feet but already 1 foot up, so 30-1

sine of the angle formed is.11.5/17.5 = ,654`31757

the angle is 41.68233314 degrees

90-that =48.91766686 degrees = half the angle that the ride is above 30 so double it

48.9 plus x 2 = 97.83533372

97.83533372/360 = .271764815= the fraction of the ride above 30

.271764815 x 8 = 2.17418527 minutes approximately, given rounding errors