Question

A radar used to detect the presence of aircraft receives a pulse that has reflected off an object 5 ✕ 10−5 s after it was transmitted. What is the distance (in m) from the radar station to the reflecting object?

Answer 1

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

$t=5\cdot 10^{-5}s$

Electromagnetic waves travel in a vacuum at the speed of light, which is equal to

$c=3.0\cdot 10^8 m/s$

Since the electromagnetic wave travels with constant speed, we can use the equation for uniform motion ,so:

$d=vt$ (1)

where

$v=c=3.0\cdot 10^8 m/s$

$t=5\cdot 10^{-5}s$

$d=2L$, where L is the distance between the radar and the object

Re-arranging eq(1) and substituting, we find L:

$L=\frac{vt}{2}=\frac{(3.0\cdot 10^8)(5\cdot 10^{-5})}{2}=7500 m$