Concept explainers
To calculate: The coordinates of the explosion if station A detects the explosion 4 seconds before station B.
Answer to Problem 52E
The coordinates of the explosion are
Explanation of Solution
Given information:
Two listening stations A and Bare located at
Formula used:
The equation of horizontal hyperbola is
Calculation:
Consider two listening stations A and B are located at
Observe that it is in shape of hyperbola whose transverse axis is horizontal.
Since, station A detects the explosion first let A be the foci of the hyperbola and hyperbola is centered at origin.
Now station B is located 1100 feet away from station A, so explosion occurs on the line
Recall that the equation of horizontal hyperbola is
Here center is origin so
Since, it took 4 seconds for sound to travel from A to B, so,
Use the
Now, substitute
Now, the explosion occurs on the line
Now, the explosion must be away from the station B than the station A, so explosion must occur in fourth quadrant. Therefore,
Thus, the coordinates of the explosion are
To calculate: The coordinates of the explosion if station A detects the explosion 1 second before station C.
Answer to Problem 52E
The coordinates of the explosion are
Explanation of Solution
Given information:
Two listening stations A and C are located at
Formula used:
The equation of horizontal hyperbola is
Calculation:
Consider two listening stations A and B are located at
Observe that it is in shape of hyperbola whose transverse axis is horizontal.
Since, station A detects the explosion first let A be the foci of the hyperbola and hyperbola is centered at origin.
Now station B is located 1100 feet away from station A, so explosion occurs on the line
Recall that the equation of horizontal hyperbola is
Here center is origin so
Since, it took 4 seconds for sound to travel from A to B, so,
Use the
Now, substitute
Now, the explosion occurs on the line
Now, the explosion must be away from the station B than the station A, so explosion must occur in fourth quadrant. Therefore,
Thus, the coordinates of the explosion are
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning