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# hw39 - homework 39 Turner(58185 This print-out should have...

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This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A flowerpot is knocked off a balcony 25 . 5 m above the sidewalk and falls toward an un- suspecting 1 . 64 m tall man who is standing below. How close to the side walk can the flower pot fall before it is too late for a warning shouted from the balcony to reach the man in time? Assume that the man below requires 0 . 249 s to respond to the warning, and the velocity of sound in air to be 344 m / s. The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 8 . 02803 m. Explanation: Let : v s = 344 m / s , H = 25 . 5 m , h m = 1 . 64 m , and t r = 0 . 249 s . h 2 = gt 2 2 /2 t 2 = t - t 1 h = H - h m t = (2 h / g ) 1/2 h 1 = h - h 2 t 1 = t r + t s h m h m H H 1 The distance from the balcony to the man’s head is h = H h m , The time for a warning to travel this dis- tance is t s = h v s = H h m v s . The total time needed to receive the warn- ing and react is t 1 = t s + t r = H h m v s + t r , and the time for the pot to fall this distance (starting from rest) is t = radicalBigg 2 h g = radicalBigg 2 ( H h m ) g . Thus the latest the warning can be sent is at t 2 = t t 1 = radicalBigg 2 ( H h m ) g H h m v s t r = radicalBigg 2 (25 . 5 m 1 . 64 m) 9 . 8 m / s 2 25 . 5 m 1 . 64 m 344 m / s 0 . 249 s = 1 . 88831 s into the fall. In this time the pot has fallen a distance of h 2 = 1 2 g t 2 2 and the corresponding height above the side- walk is H 1 = H h 2 = H 1 2 g t 2 2 = 25 . 5 m 1 2 ( 9 . 8 m / s 2 ) (1 . 88831 s) 2 = 8 . 02803 m . 002 10.0 points Sound waves travel through a liquid of density 9240 kg / m 3 at a speed of 4440 m / s. What is the bulk modulus of this liquid? Correct answer: 1 . 82154 × 10 11 Pa. Explanation: Let : ρ = 9240 kg / m 3 and v sound = 4440 m / s . homework 39 – Turner – (58185) 1

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hinojosa (jlh3938) – homework 39 – Turner – (58185) 2 In fluids, sound waves are pressure waves, and their speed depends on the fluid’s density and bulk modulus: v sound = radicalBigg B ρ . For the liquid in question, we know the density and the speed of sound, so the bulk modulus is B = ρ v 2 sound = (9240 kg / m 3 ) (4440 m / s) 2 = 1 . 82154 × 10 11 Pa . 003 10.0 points A harmonic wave y = A sin[ k x ω t φ ] , where A = 1 m, k has units of m 1 , ω has units of s 1 , and φ has units of radians, is plotted in the diagram below. +1 1 A (meters) t (seconds) 10 20 30 At the position x = 0 Which wave function corresponds best to the diagram? 1. y = A sin bracketleftbigg k x parenleftbigg 2 π 15 s parenrightbigg t parenleftbigg 2 π 3 parenrightbiggbracketrightbigg 2. y = A sin bracketleftbigg k x parenleftbigg 2 π 15 s parenrightbigg t parenleftbigg 1 π 3 parenrightbiggbracketrightbigg 3. y = A sin bracketleftbigg k x parenleftbigg 2
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hw39 - homework 39 Turner(58185 This print-out should have...

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