A cowboy in an old western movie is rescuing a damsel in distress tied to a trai

Question

A cowboy in an old western movie is rescuing a damsel in distress tied to a train track, but a train is on the way! His partner has his ear to the iron train tracks, listening for the train. (Iron has a Young's modulus of 21×1010Pa and a density of 7.874g/cm3 .) His partner is first able to hear the sound from the train when it is 11.8 km away.

A.) How long does it take for this sound from the train to reach his partner?

B.) If the train is moving at constant speed   22.6 m/s   , how much time does the cowboy have from when his partner warns him to rescue the damsel and get safely out of the way?

C.) The director decides to have the cowboy listen for the train as he is freeing the damsel. Since the sound dissipates more in air than in the solid tracks, the cowboy can't hear the train until it whistles when it is only   2.5 km    away. If the air temperature is   20.9 C    , how long does it take for the sound to reach the cowboy, propagating through the air? Use =1.40 , and the molar mass of air is 28.8103kg/mol .

D.) How long does the cowboy have to rescue the damsel between when he hears the train and when it reaches him?

Thanks.

Explanation / Answer

a)

Speed of sound in air is 5130 m/s

Time taken to reach is t = 11.8*1000/5130 = 23 seconds

b)

Given Train is moving at a speed of 22.6m/s

Time available = 118000/22.6 =5221.2 seconds

c)

Time taken = 25000/22.6 = 1106 seconds

d)Time available = 5221.1-1106 =4115 seconds

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