Question

Serena Williams Due January 16 at 9 a.m. The Global Positioning System allows for the location on Earth's surface to an accuracy of a few meters. Satellites orbit Earth at locations that are known accurately. They transmit a signal that conveys which satellite it is, its location, and the time the signal was sent. Suppose the ith satellite is located at x, Vi, and z and it broadcasts its signal at time t,. The receiver is located at (x.y.:) and receives the signal at time t Since the radio signal propagates at the speed of light, c, the distance from the th satellite to the receiver must satisty There are four satellites, so there are four equations just like equation (1). There are four unknowns: xy.z and t so when the signals from four satellites are received, the four simultaneous equations can be solved for the location. Unfortunately we may not know how to solve simultaneous non-linear equations. We can make the problem more tractable if we consider two "satellites" or towers and only use one dimension. Then there are two equations and we can linearize them by taking the square root of each side (Careful! Taking a square root involves + and -signs). Suppose the towers send information in the following format (satellite #, satellite location (miles), time signal sent (us)) The towers are located along the x-axis. tower # l is located at xi and tower #2 is located at X2. You are Chase of the Paw Patrol somewhere on x axis. X2 1. At time 341.980us you receive the following signals:(1, -13.5000, 260.668 and (2, 20.0000, 246.412 (A Convert the locations in miles to locations in feet and the times in microseconds to nanoseconds. The speed of the radio signal is the speed of light, c, which happens to be 299,792,458 m/s exactly. For our purposes take the speed of light to be exactly Ift/ns to make the math easier. Show your work here. Satellite Location (ft) Time (ns

if you could do these for me that's be great there really easy I just want to make sure I did them right

Answer 1

c: 1시ns . 2. Tolh S pPp 2. 2- 280-*)^= (266668-3h1980)-' 2.2 2. χ 201,68, 10032 LM