Assume base station sends a signal at T = 0 micro sec. A UE which is at a distance ‘d’ from the base station receives the signal and immediately responds back without any delay. Base station receives the response at T = 1 milli seconds.
How far is the UE from the base station?
Since the signal travels to UE and then back
The distance from the Base station to UE = d
The distance from UE to the Base station = d
hence total distance cover by the signal= 2d (since the signal travels from the Base station to UE ad then back)
The signal takes 1 milli-second to travel 2d
As we know that 1 milli-second = 1*10^(-3)sec
and the speed of light = 3*10^8m/s
we also know that Velocity of the signal=Distance travelled/ Time taken
hence Distance travelled= Velocity of the signal*Time taken
therefore : 2d=(3*10^8)*(1*10^(-3))
The distance between the UE and the base station can be calculated by using the total time taken for the signal to travel from the base station to the UE and back. As we know that the base station receives the response signal at T = 1 milli seconds (10^-3 seconds) after sending the initial signal.
It will take T/2 time to cover distance ‘d’ .
The distance ‘d’ can be calculated as
d = c * T/2
where d is the distance, c is the speed of light, and T is the total time taken for the signal to travel from the base station to the UE and back.
Substituting the values,
d = (3 x 10^8 m/s) * (10^-3 s)/2 = 1.5 x 10^5 meters
Therefore, the UE is approximately 150,000 meters or 150 km away from the base station.
The distance between UE and base station is 150km .
Since the signal takes 1 milli second to travel 2d distance (Basestation to UE : ‘d’ , UE to Basestation: distance ‘d’),
d = 1 milli sec * c/2 where c is speed of light
d = 150km
Since signal takes 2d distance because it travels from base station to ue and vice versa’
So speed =distance/time
Total distance = 2d (sent + received)
speed of light = 3 * 10^8
time = 1 milli sec = 1*10^-3
distance = velocity * time
2d = 3*10^8 * 1*10^-3
Distance covered= 2d
Speed= 3×10^8 m/s
Distance travelled by the signal ( to and fro)= 2d
Time taken to travel = 1 millisecond
velocity of signal = distance travelled / time taken
As these signals are electromagnetic, they travel with the velocity of light in free space.
Hence taking Velocity = 3*10^8 m/s
2d = 3*10^8*10^(-3)
d = 150 kms.
The distance between UE and the base station is d.
The distance travelled by the signal from base station to UE and again from UE to base station=d+d=2d.
The signal takes 1 milli second to travel 2d distance.
From Base station to UE : ‘d’
From UE to Base station : ‘d’
We know that
Distance = speed *time
2d = 3*10^8*1*10^-3
Speed of light = 3*10^8
d = 150 km
The distance between UE and Base Station is 150km
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The distance from UE to base station is d.
And the distance from base station to UE is d
Therefore total distance = 2d
We know that distance = speed * time
Time = 1 milli second (given)
Speed = 3 * 10 ^ 8.
2d=3*10 ^8 * 10^(-3)
2d = 300 Kilometers.
d = 150 kilometres.
The signal covers 2 times the distance.
2*Distance = (Speed of EM wave) * 1mSec = 3*10^8m/sec * 10^-3sec = 300Km
So the distance covered = 300/2 = 150Km.
Distance travelled from UE to base station =d
Distance travelled from base station to UE=d
Total distance travelled=2d
Velocity (v) =Distance travelled(d)/ Time taken(t)————(1)
Speed of light = 3 * 10 ^ 8
Time taken=1 milli second (given)
2 d= (3 * 10 ^ 8)* 10^(-3)