A fire helicopter carries a 620kg bucket of water at the endof a 20m long cable.

Question

A fire helicopter carries a 620kg bucket of water at the endof a 20m long cable. As the aircraft flies back from a fire at aconstant speed of 40 m/s, the cable makes an angle of 40 degreeswith respect to the vertical. a.) Determine the force of air resistance on the bucket. b.) After filling the bucket with sea water, the pilot returnsto the fire at the same speed with the bucket now making an angleof 7 degrees with the vertical. What is the mass of the water inthe bucket. Please show all work for full points A fire helicopter carries a 620kg bucket of water at the endof a 20m long cable. As the aircraft flies back from a fire at aconstant speed of 40 m/s, the cable makes an angle of 40 degreeswith respect to the vertical. a.) Determine the force of air resistance on the bucket. b.) After filling the bucket with sea water, the pilot returnsto the fire at the same speed with the bucket now making an angleof 7 degrees with the vertical. What is the mass of the water inthe bucket. Please show all work for full points

Explanation / Answer

T sin = F   where T is the tension in thecable and F the air resistance T cos = m g     where m is the massof water in the bucket tan = F / (m g)   dividing 1st equation bythe 2 nd F = m g tan = 620 * 9.8 * tan 40 = 5098 N Rewriting the equation m = F / (g tan ) = 5263 / (9.8 *tan 7) = 4374 kg Something is wrong with this problem - either somethingheavier than seawater is in the bucket or the given angles are wrong.

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