Question

A radar sends a signal to an aeroplane at a distance $45km$ away with a speed of $3\times {10}^{8}m{s}^{-1}$. After how long is the signal received back from the aeroplane?

Answer 1

Step 1 Given:

Distance between radar and aeroplane $=45km$

$=45\times {10}^{3}m$

Speed of sound $=3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Step 2. Finding the speed of the sound

$Time=\frac{TotalDis\tan ce}{Speedofsound}$

$\because$Signal go from radar to the aeroplane and then, came back from the aeroplane to radar. So, the total distance travelled by the signal will be two times of the distance between the RADAR and aeroplane.

$Timetoreceivethesignalback=\frac{2(Dis\tan cebetweentheaeroplaneandradar)}{Speedofthesound}$

$\therefore$ Time to receive a signal back $=\frac{2\times 45\times {10}^3}{3\times {10}^8}$

$=\frac{90\times {10}^3}{3\times {10}^8}$

$=3\times {10}^{-4}sec$

Hence, radar receives the signal in $3\times {10}^{-4}$ sec.