Ferris Wheel Trig Question

Question

Jamie rides a Ferris wheel for five minutes. The diameter of the wheel is 10 meters,
and its center is 6 meters above the ground. Each revolution of the wheel takes 30 seconds.
Being more than 9 meters above the ground enables Jamie to see the ocean. For how many
seconds does Jamie see the ocean?

Answer 1

Hi Gnarls,

 

This is another one of those questions where I wish I could share my drawing with you.

 

The point where Jamie is 9 meters above the ground forms a right triangle with one vertex at the center of the wheel, with hypotenuse being the radius of the wheel (r = 10/2 = 5 meters), and one side being 3 meters (this is because when it gains an elevation of 3 meters from the level of the center. We can calculate the angle between this side and the radius using the sine function.

sin theta = 3/5 = 0.6 

theta = 37 degrees (rounded to the nearest whole number)

 

37*2 = 74 degrees since there will be another triangle on the other side of the center.

180-74 = 106 degrees (out of 360 deg when he will be higher than 9 meters and be able to see the ocean)

For a given revolution, this is equal to 106/360*30 = 8.8 seconds

5*60/30 = 10 total revolutions

10*8.8 = 88 seconds he will see the ocean.

 

Message me if you want to see my drawing.