Wheel Lift

Wheel Lift
The diameter of a wheel that moves the cable of a a ski lift is 5.75m. Through what angle does the wheel have?

The diameter of a wheel that moves the cable of a a ski lift is 5.75 m. Through what angle does the wheel have to move advance one of the chairs a distance of 10 meters?

In order for the wheel to move the chair 10 meters, the wheel must reel in 10 meters of the rope.

Using s = rθ, the angle required (in radians) is:
10 = (5.75/2)θ
==> θ = 20/5.75 radians.

In degrees, this is 20/5.75 * 180/π ≈ 199.3°.

I hope this helps!

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