Taking the speed of the radio signal as 3×108 m/s, calculate the time taken for a signal to reach a GPS receiver from a GPS satellite at a position 21 000 km distant from the receiver. Assume that the speed of the signal is unchanged over the whole path length. Express your answer in milliseconds
To calculate the time taken for a signal to reach a GPS receiver from a GPS satellite at a distance of 21,000 km, we need to use the formula:
Time = Distance / Speed
Here, the distance is given as 21,000 km. However, we need to convert this distance into meters because the speed of the radio signal is given in meters per second.
1 km = 1000 m
So, the distance in meters would be:
21,000 km * 1000 m/km = 21,000,000 meters
Now, we can substitute the values into the formula:
Time = 21,000,000 meters / (3 x 10^8 m/s)
Calculating this, we get:
Time = 70 milliseconds
Therefore, the time taken for a signal to reach a GPS receiver from a GPS satellite at a position 21,000 km distant is 70 milliseconds.
d = V*t = 21*10^6 m.
t = 21*10^6/3*10^8 = 7*10^-2 s. = 70 ms.