How far is the plane from the radar if the sent signal returned back after 400 μs?

Given:

t = 400 μs – time interval during which the sent signal from the radar returned back;

c = 3 * 108 meters / second – the speed of propagation of electromagnetic waves.

It is required to determine L (meter) – at what distance the aircraft is from the radar.

Let’s convert the units of measurement of time to the SI system:

t = 400 μs = 400 * 10-6 seconds = 4 * 10-4 seconds.

According to the condition of the problem, the signal from the radar reached the plane, and then reflected from it, returned back. Then, the total traversed signal path will be equal to:

S = 2 * L.

We find the distance to the plane from the following formula:

S = c * t;

2 * L = c * t;

L = c * t / 2 = 3 * 108 * 4 * 10-4 = 12 * 108 – 4 = 12 * 104 = 120,000 meters (120 kilometers).

Answer: the plane is 120 kilometers from the radar.