Question

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 5 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 22 meters above the ground

Answer 1

Answer:

The ride is above 22m in height for 1.33 minutes.

Explanation:

Let's first find the height required above the boarding platform for the ride to be 22 m above the ground:

Height required = 22 - 5 = 17 m

We can now, using a right angled triangle of height equal to the Ferris wheel radius, calculate the angle from the vertical axis to achieve this height:

Height of triangle = 15 - (17 - 15) = 13 m

Hypotenuse of triangle = radius = 15 m

Angle from the vertical:

Cos( Angle ) = base / hypotenuse = 13 / 15

Angle = 29.92 °

Multiplying this angle by 2 we get the total angle through which the ride is at the required height:

Total Angle = 29.92 * 2 = 59.85 °

To take out the time we can now simply multiply the ratio of this angle /360 by the time taken for one complete revolution:

Time = $\frac{59.85}{360} * 8$

Time = 1.33 minutes