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 x 10⁸ m s^-1.

Given,

Distance d = 300 km,

Velocity V = 3 x 10⁸ m s^-1

If it takes time t for the signal to go up to the enemy plane and come back, then

$V = \dfrac{2d}{t} \\[0.5em] \Rightarrow t = \dfrac{2d}{V} \\[0.5em] = \dfrac{2 \times (300 \times 10^3 m)}{3 \times 10^8 m s ^{-1}} \\[0.5em] = 2 \times 10^{-3} \text{ s}$

Hence, the radar will detect the enemy plane in 2 x 10^-3 s