A Ferris wheel has radius of 5 inches and center is 6.5 inches above the ground. It turns once every 30 seconds. What is the height of a point on this Ferris wheel at the 8'o clock position?

Question

Find the height of the 8'o clock position.

Answer 1

On a clock face each hour division is 360/12=30°.

8 o’clock is therefore 60° from 6 o’clock, the lowest position.

If O is the centre of the wheel, P the lowest point and Q the 8 o’clock position then the perpendicular QN onto OP is such that ON=OQcos60=5/2=2.5in, because OQ=OP=5in. Therefore NP=OP-ON=2.5in and the height of Q from the ground is 2.5+(6.5-5)=4in.