Explanation Definition used: Equation of a Hyperbola: Center at ( 0 , 0 ) ; Transverse axis along the x-axis: An equation of the hyperbola with the center at ( 0 , 0 ) , foci at ( − c , 0 ) and ( c , 0 ) , and vertices at ( − a , 0 ) and ( a , 0 ) is x 2 a 2 − y 2 b 2 = 1 where b 2 = c 2 − a 2 . The hyperbola has a transverse axis of length 2 a along x axis and a conjugate axis at ( 0 , ± b ) of length 2 b . “ Equation of a Hyperbola: Center at ( 0 , 0 ) ; Transverse axis along the y-axis An equation of the hyperbola with the center at ( 0 , 0 ) , foci at ( 0 , − c ) and ( 0 , c ) , and vertices at ( 0 , − a ) and ( 0 , a ) is y 2 a 2 − x 2 b 2 = 1 where b 2 = c 2 − a 2 . The hyperbola has a transverse axis of length 2 a along y axis and a conjugate axis at ( ± b , 0 ) of length 2 b . Calculation: Assume that the coordinate ( x , y ) be the location of the explosion and let the two persons be standing the two foci. It is given that the two persons are 1000 m apart. That is, 2 c = 1000 c = 500 Thus, the coordinates of the persons is ( ± 500 , 0 ) . Let u be the sound of the explosion and t be the time between the explosion and the time the first person hears the explosion. Also, one person heard 4 seconds before the other person. That is, the second person hear it at the t + 4 second. Use the distance formula to obtain the distance between ( x , y ) to ( 500 , 0 ) and ( x , y ) to ( − 500 , 0 ) as follows: d 1 = ( x − 500 ) 2 + ( y − 0 ) 2 t u = ( x − 500 ) 2 + y 2

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 21.6, Problem 46E

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To explain: The reason why the location of the explosion is on one of the points of a hyperbola.

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Chapter 21.6, Problem 45E

Chapter 21.6, Problem 47E

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Chapter 21 Solutions

Basic Technical Mathematics

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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