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p0222

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Unformatted text preview: .................................................... ......................................................................... ......................................................................... ......................................................................... ......................................................................... ......................................................................... ......................................................................... ......................................................................... ......................................................................... ......................................................................... ......................................................................... ......................................................................... ......................................................................... s a g = gk So ut on: To so ve h s prob em we proceed n hree s eps F rs we de erm ne he me akes for he s one o fa from he op of he we o he surface of he wa er t1 Then we so ve for he me akes for he sound wave o rave from he surface of he wa er o he op of he we t2 F na y we se = t1 + t2 Stone fa ng from the top of the we to the surface of the water: The s one fa s under he ac on of grav y The equa on govern ng s mo on s m d2 z = mg dt2 z(0) = 0 z(0) = 0 where we no e ha he s one s ar s from z = 0 w h vz = z = 0 The so u on s z(t) = Deno ng he d s ance from he op of he we s one o reach he surface of he wa er s 1 2 gt 2 akes for he o he surface of he wa er by s he me t1 = 2s g Sound wave trave ng from the surface of the water to the top of the we : The sound wave propaga es a he speed of sound and s mo on s governed by dz = -a dt The so u on for he pos on of he wave fron s z(t) = s - at The wave fron reaches he surface when z = 0 wherefore t2 = s a z(0) = s 96 So, the total time, , is = t1 + t2 = CHAPTER 2. PARTICLE KINEMATICS 2s s + g a We are given a = 1160 ft/sec and s = 500 ft. Thus, the time is = 2(500 ft) 32.174 ft/sec 2 + 500 ft = 5.575 sec + 0.431 sec = 6.0 sec 1160 ft/sec Note that only 7.2% of the total time corresponds to the sound wave traveling from the surface of the water to the top of the well....
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