An enemy plane is at a distance of 300 km from a radar. In how much time the radar will be able to detect the plane? Take velocity of radio waves as 3 × 108 m s-1.

Given: distance to the plane d = 300 km = 3 × 10⁵ m

speed of radio waves c = 3 × 10⁸ m s⁻¹

The radar signal must travel TO the plane and back, so total distance = 2d = 2 × 3 × 10⁵ = 6 × 10⁵ m

Time, t = total distance ÷ speed = (6 × 10⁵) ÷ (3 × 10⁸) = 2 × 10⁻³ s

The radar detects the plane in 2 × 10⁻³ s (0.002 s).

Radar, SONAR and echo questions all share one idea: the signal makes a ROUND TRIP. The detector only knows the plane is there once the reflected signal comes back, so the distance travelled is 2d, not d.

Forgetting the factor of 2 gives 1 × 10⁻³ s — the standard wrong answer. Convert the kilometres to metres too, since the speed is in metres per second.

The general form worth memorising: for any echo or reflection, 2d = v × t.