Question

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

Answer 1

Step 1: Given data:

The distance between the plane and the radar is $d=300km$

Velocity of radiowaves $=3\times {10}^{-8}m{s}^{-1}.$

Step 2: Calculation of the distance travelled by the radio wave,

As we know,

The radio waves first, reach the plane, and then they get reflected by the plane.

The reflected radio waves then reach the radar where they will be detected by the radar.

Hence, we can conclude that the radio waves have to travel twice the distance between the plane and the radar.

So, the distance travelled by the radio wave will be

$$\begin{gathered} D=2d \\ =2\times 300 \\ =600km. \\ =600\times {10}^{3}m \end{gathered}$$

Step 3: Calculation of the time taken by the radar to detect the plane,

As we know, the time taken by the radar to detect the plane can be determined by the formula: $t=\frac{D}{v}$

Where, $D$ is the distance travelled by the radio wave and $v$ is the velocity of the radio wave.

Thus, the time taken by the radar to detect the plane will be

$$\begin{gathered} =t=\frac{600\times {10}^3}{3\times {10}^8} \\ \Rightarrow =\frac{600\times {10}^3}{300\times {10}^6} \\ \Rightarrow =2\times {10}^{-3}sec. \end{gathered}$$

Hence, the time taken by the radar to detect the plane will be $2\times {10}^{-3}sec.$