Question

An enemy plane is at a distance$300km$ from the radar. In how much time, the radar will be able to detect the plane? (Take, the velocity of radio waves as $3\times {10}^{8}m{s}^{-1}$)

Answer 1

Step 1: Given data and diagrammatic representation:

The distance(d) between the enemy plane and the radar =$300km$

Step 2: Calculation of time (t):

Formula used:

$$\begin{gathered} Velocityofradiowave=\frac{Dis\tan ce}{Time} \\ Time=\frac{Dis\tan ce}{Velocity} \end{gathered}$$

Since the wave has to travel from radar to target and return from target to radar.

Hence, the distance traveled by the wave will be doubled i.e. distance$=d+d=2d$

$\Rightarrow t=\frac{2d}{v}$

$$\begin{gathered} \Rightarrow t=\frac{2\times 300\times {10}^3}{3\times {10}^8} \\ \Rightarrow t=2\times {10}^{-3}s \\ \Rightarrow t=2millisecond \end{gathered}$$

Hence the time taken to detect the plane is$2milliseconds$.