Question

A radar is able to detect the reflected waves from an enemy aeroplane, after a time interval of $0.02ms$. If the velocity of the waves is $3\times {10}^8{\mathrm{ms}}^{-1}$. Calculate the distance of the plane from the radar.

Answer 1

Step 1: Given data:

Time interval $\left(\mathrm{t}\right)=0.02milli-seconds$ $=2\times {10}^{-5}Sec$
Velocity $\left(v\right)=3\times {10}^8\mathrm{m}{\mathrm{s}}^{-1}$

Step 2: Calculating the distance from the RADAR:

As the distance traveled by the wave is twice the distance between energy and source.$=2d$
Now, Applying the formula,

$Dis\tan ce\left(2d\right)=velocity\left(v\right)\times time\left(t\right)$

or $t=\frac{2\mathrm{d}}{v}$

Substitute the value in the above equation we get,
$2\times {10}^{-5}=\frac{2\mathrm{d}}{3\times {10}^8}$
$6\times {10}^{-5}\times {10}^8=2\mathrm{d}$

$\mathrm{d}=\frac{6\times {10}^3}{2}=3\times {10}^3=3000m$

or $d=3\mathrm{km}$
Hence, the distance of the plane from the radar is $3\mathrm{km}$.