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 concepts. To practice quantitative skills related to systems of equations and coordinate systems. Instructions List, on the first page, any students with whom you worked and/or any outside resources you used in preparing your solutions. You may not consult solutions to previous semesters' assignments. Clearly identify which problem you are solving at the start of the solution. Solutions must be clearly and logically presented. When applicable, show your work! The solution to each problem must be continuous; that is, parts should not be crossed out and solutions to other problems should not be interspersed. Your solutions must be submitted through Blackboard as a single PDF file. Improperly submitted or late homework will not receive credit. Grading Policy This assignment will be graded for both completeness and accuracy. Completion of the assignmentdid you attempt every problem?will be worth 50% of the score. The problems will also be graded for accuracy; that is, did you provide a correct answer and, when applicable, show your work? Accuracy will determine the remaining 50%. Remember, if you use Wolfram Alpha (or another software tool), include a screen shot with both input and pertinent output to show your work. Also, wikipedia is not a valid source (although it may be a great starting point to find more acceptable sources!). Problems 1. (?, 16 pts) How does a GPS receiver know the locations of the satellites when determining its location? Hint: The Trimble tutorial might be useful. 2. (??, 26 pts) Meteorites regularly enter the atmosphere, where they heat up, disintegrate, and finally explode before hitting the surface of the Earth. Such an explosion generates a shock wave (traveling at the speed of sound) that can be detected by seismographs installed at various locations on the Earth's surface. Each seismograph (equipped with a perfectly synchronized clock) then determines the time it took the shockwave to reach the seismograph. How many seismographs need to detect the shock wave to determine the location of the meteorite explosion? 3. (?, 16 pts) For each of the following systems of equations, (i) determine the number of equations and the number of unknown variables in the system and (ii) classify the system as consistent or inconsistent. If the system is consistent, (iii) solve the system. Homework 1: GPS Page 2/2 Hint: items (ii) and (iii) are closely related; Wolfram Alpha may be useful. (a) |x + 7| = 9, |x + 1| = 3, |x 4| = 2. (b) p 2q = 5, p + 2q = 1, p q = 3. 4. (?, 16 pts) Calculate the latitude and longitude angles for the following Cartesian coordinates. (a) (x = 2, y = 7, z = 1). (b) (x = 5, y = 1, z = 3). 5. (??, 26 pts) The following table shows the locations of satellites and their distances from you. All coordinates and distances are in miles. Satellite x y z 1 4608.6 6581.76 9575.56 2 2162.34 12263.3 1089.45 3 9430.08 7912.78 2170.6 Distance 8700.78 11447.6 11568.6 (a) Determine if each of the following points could be your location. Justify why or why not. (b) If you know you are also on the surface of the Earth (assume radius is 4000 mi), what is your location? If unknown, explain why. (i) (x = 476.824, y = 2065.35, z = 3392.19). (ii) (x = 2264.84, y = 11859.9, z = 10350.6)