# A cable car at a ski resort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m Assuming no slippage , how fast must the pulley rotate for...

A cable car at a ski resort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m Assuming no slippage , how fast must the pulley rotate for the cable car to make the trip in

12 minutes?

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### 1 Answer

The cable car at a ski resort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. It can be assumed that there is no slippage as the cable moves over the pulley.

As the diameter of the pulley is 3 m, its circumference is `pi*d = 3*pi` . If the pulley rotates n times, for the entire trip of 6.8 km

`n*3*pi = 6800`

=> `n = 6800/(3*pi)`

As the trip has to be completed in 12 minutes, the pulley rotates at `(6800/(3*pi))/(12*60) ~~ 1` rotation/second.

If the pulley completes 1 rotation in a second, the entire trip of 6.8 kilometer will be completed in 12 minutes.