Question: In the LORAN (Long Range Navigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship or an

In the LORAN (Long Range Navigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference |PA| - |PB|, and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). Suppose that station B is located 400 mi due east of station A on a coastline. A ship received the signal from B 1200 micro seconds (us) before it received the signal from A.
(a) Assuming that radio signals travel at a speed of 980 ft/us, find an equation of the hyperbola on which the ship lies.
(b) If the ship is due north of B, how far off the coastline is the ship?

coastline 400 mi transmitting stations

Step by Step Solution

★★★★★

3.50 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Set up the coordinate system so that A is 200 0 and B ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

786-C-P-E (252).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

In Fig P2.40 the pressures at A and B are the same, 100 kPa. If water is introduced at A to increase pA to 130 kPa, find and sketch the new positions of the mercury menisci. The connecting tube is a...

A beam ABC with simple supports at A and B and an overhang BC supports a concentrated load P at the free end C (see figure). (a) Determine the strain energy U stored in the beam due to the load P....

A beam rests on supports at A and B and is loaded by a distributed load with intensity q as shown. A small gap Î exists between the unloaded beam and the support at C. Assume that span length L...

51. In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at and transmit simultaneous signals to a ship or an aircraft located at . The onboard computer converts...

3. (Inspired by Armendariz & Daniels, p. 40) In the early 1600s, Johannes Kepler proposed three laws of planetary motion, based upon data carefully collected by his mentor, Tycho Brahe. Kepler's 3'd...

When you have finished, please submit this test to the dropbox. Using methods learned in our class, all steps to The answers are required to be shown for credit For reference, our recording for the...

1. Graph the ellipse. (x-2)- (v+1) + 9 36 Name the coordinates of the center, endpoints of major axis, endpoints of minor axis, and foci of the ellipse. Answer.2. LORAN is a long range hyperbolic...

Two major themes from the introduction to module 4 are "Project Management" and "Managing Risk." Discuss, in depth, your analysis of the company's actions in relation to the concepts of these two...

1: GPS AMS 103, Spring 2017 Due: Thursday, February 9, 11:59 pm EST Quiz: Tuesday, February 14, in class Objectives To reinforce concepts relevant to GPS technology and the underlying mathematical...

Find the sales tax and total sale. Item marked price Sales tax rate $738.47...........................6%

Solve the linear programming problem in Problem using the simplex method Maximize subject to P = x1 +x2 +2x3 x1 - 2x2 + x3 9 2x1 + x2 + 2x3 28 x1,x2,x3 0

A manufacturer of designer jeans must decide whether to build a large factory or a small factory in a particular location. The profit per pair of jeans manufactured is estimated as $10. A small...

Prisons 2013 A report from the U.S. Department of Justice (www.ojp.usdoj.gov/bjs/) reported the percent changes in federal prison populations in 20 northeastern and midwestern states from 2000 to...

Find the area of the surface. The part of the surface 2y + 4z x 2 = 5 that lies above the triangle with vertices (0, 0), (2, 0), and (2, 4).

Evaluate the iterated integral. /2 (2x (x+z cos(x 2y + z) dy dz dx

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. (x+Jy) sin(xy)dx dy

Wii Brothers, a game manufacturer, has a new idea for an adventure game. It can market the game either as a traditional board game or as an interactive DVD , but not both. Consider the following cash...

For an interest rate of 2% per quarter, compounded continuously, the effective semiannual interest rate is closest to A. Less than 4.0% B. 4.02% C. 4.12% D. Over 4.25% A steel fabrication company...

Capital Budgeting Criteria: Mutually Exclusive Projects A firm with a WACC of 10% is considering the following mutually exclusive projects: O 1 N 3 4 5 $55 $230 + Project 1 -$400 $55 $55 Project 2 -...