A Ferris wheel radius is 5 in. and center is 6.5 in. above the floor. It turns once every 30 seconds. How high would a point be 21 sec. after passing the 3 o'clock position turning counter clockwise?

Question

Find the height 21 seconds after passing the 3 o'clock position turning counter clockwise

Answer 1

Let h = the height of the point from the floor after 21 seconds.

T = 3 o'clock position

EO = 5 ft.

(21/30)•(360°) = 252º

After 21 seconds, the ferris wheel has turned 252º.

360º - 252º = 108º left to make a full rotation.

θ = 108º -90º =18º

sin (18º) = EA/EO

EA = 5•sin (18º)

h = EA + 6.5 = 5•sin (18º) + 6.5

h ≈ 8.05 in.