Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Question
Chapter 10.4, Problem 46E
To determine
To write: The equation of the hyperbola on which the lightning strike was located, if sound travels at 1100 feet per second.
Expert Solution & Answer
Answer to Problem 46E
Explanation of Solution
Given information: Forestry: Two ranger stations located 4 miles apart observe a lightning strike. A ranger at station A reports hearing the sound of thunder 2 seconds prior to a ranger at station B . place the two ranger stations on the x -axis with the midpoint between the two stations at the origin. The transverse axis is horizontal.
Calculation:
By the definition of the hyperbola we know the difference of the distances between the towers and the lightning strike = the distance between the vertices
The difference was 2 seconds between the towers.
Since sound travels at 1100 feet/sec. The difference would be 2200 feet.
Since we’re centered at the origin, this makes
We know the distance between the foci is 4 miles.
5280 feet = 1 mile means 21.120 feet.
This means c = 10,560 feet.
If
Therefore equation is:
Chapter 10 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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