Answer:
7500 m
Explanation:
The radar emits an electromagnetic wave that travels towards the object and then it is reflected back to the radar.
We can call L the distance between the radar and the object; this means that the electromagnetic wave travels twice this distance, so
d = 2L
In a time of
[tex]t=5\cdot 10^{-5}s[/tex]
Electromagnetic waves travel in a vacuum at the speed of light, which is equal to
[tex]c=3.0\cdot 10^8 m/s[/tex]
Since the electromagnetic wave travels with constant speed, we can use the equation for uniform motion ,so:
[tex]d=vt[/tex] (1)
where
[tex]v=c=3.0\cdot 10^8 m/s[/tex]
[tex]t=5\cdot 10^{-5}s[/tex]
[tex]d=2L[/tex], where L is the distance between the radar and the object
Re-arranging eq(1) and substituting, we find L:
[tex]L=\frac{vt}{2}=\frac{(3.0\cdot 10^8)(5\cdot 10^{-5})}{2}=7500 m[/tex]
The distance from an object is required.
The object is 7500 m from the radar.
Time to transmit or receive a the signal is
[tex]\dfrac{t}{2}[/tex]
where
t = Total time taken to transmit and receive = [tex]5\times 10^{-5}\ \text{s}[/tex]
c = Speed of radio signal = [tex]3\times 10^8\ \text{m/s}[/tex]
Distance is given by
[tex]d=\dfrac{t}{2}c\\\Rightarrow d=\dfrac{5\times 10^{-5}}{2}\times 3\times 10^8\\\Rightarrow d=7500\ \text{m}[/tex]
The object is 7500 m from the radar.
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