Question

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

Answer 1

Step 1: Given data:

Distance between the plane and radar $=300km$

Speed of the radio waves, $v=3\times {10}^{8}m{s}^{-1}$

Step 2: Formula used:

Time,$t=\frac{Dis\tan ce\left(D\right)}{velocity\left(v\right)}$

Step 3: Find the time taken by radar to detect the plane

The radio waves, at first, reach the plane. Then they get reflected by the plane and so the reflected radio waves reach the radar again where they get detected. So, radio waves have to travel twice the distance between the plane and the radar.

Distance traveled by radio waves,$D=2d$

$=2\times 300$

$=600km$

$D=600\times {10}^{3}m\left(\because 1km=100m\right)$

Now,

Time taken, $t=\frac{Dis\tan ce\left(D\right)}{velocity\left(v\right)}$

Substitute the known values

$$\begin{gathered} t=\frac{600\times {10}^3}{3\times {10}^8} \\ t=\frac{200\times {10}^3}{{10}^8} \end{gathered}$$

$t=2\times {10}^{-3}s$

Thus, the time taken by radar to detect the plane is $2\times {10}^{-3}s$.