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The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear velocity of 16 miles per hour, how fast would the pulley need to turn (in revolutions per minute)? (1 mi = 5,280 ft. Round your answer to the nearest tenth.)

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sqdancefan

Answer:

  32.0 rpm

Step-by-step explanation:

16 mi/h = (16 mi)(5280 ft/mi)/(60 min) = 1408 ft/min

One revolution is a distance of ...

  C = πd

  C = π(14 ft) ≈ 43.98 ft

So the number of revolutions per minute is ...

  (1408 ft/min)/(43.98 ft/rev) = 32.01 rev/min

The pulley needed to turn at 32.0 rpm.

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