A radar has a power of 1 Kw and is operating at a frequency of 10 GHz

A radar has a power of 1 Kw and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth = 6.4 x 106 m) is

  1. 80 km
  2. 64 km
  3. 40 km
  4. 16 km

Answer

Maximum distance on earth where object can be detected is d, then

(h + R)2 = d2 + R2

d2 = h2 + 2Rh

since h << R, d2 = 2hR

The correct option is A.