# Ferris Wheel & Pin Wheel

Brent and his sister Kim are at the fair riding on a ferris wheel. They each have a pinwheel on a stick, and Kim holds hers out to the side to spin in the breeze caused by the ferris wheel cart going through the air. Brent, having studied more physics than Kim, decides to hold his pinwheel up above his head, so the center of his pinwheel is 4 feet higher than the center of Kim’s.

When the two of them are at the top of the ferris wheel’s rotation, Kim’s pinwheel is 48 feet above the ferris wheel axis. At this point, how much faster is Brent’s pinwheel going through the air than Kim’s?

The ferris wheel rotates at a rate of two rotations per minute.

Thanks Brent for another great math riddle submission this month.

### 2 guesses to Ferris Wheel & Pin Wheel

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• anant

Brent’s pinwheel is not going to be faster than Kim’s

• Anant is today’s winner!
No faster, Brent’s pinwheel travels at the same speed as Kim’s. There is a bit of a trick to this question, in that all parts of the cart need to be traveling through the air at the same speed. If the top of the cart was traveling faster than the bottom, it would dump the people out as it rotated around the circle. So the answer to the riddle is that Brent’s pinwheel would be going through the air at the same speed (603.2 fpm) as Kim’s – and Brent’s physics classes seem to have been a waste of time and money. The speed of Kim’s pinwheel through the air can be found by determining the distance she travels through the air in a given time period. Since the circumference of the wheel is 2 x pi x r (2 x 3.1416 x 48) feet or about 301.6 feet, and it travels that distance twice per minute Kim’s pinwheel would be traveling about 603.2 feet per minute or 36,138 feet/hr or dividing by 5280 feet per mile yields 6.84 mph.