Question

Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object. (a) How far away is the planet Venus if the echo time is 1000 s? (b) What is the echo time for a car 75.0 m from a Highway Police radar unit? (c) How accurately (in nanoseconds) must you be able to measure the echo time to an airplane 12.0 km away to determine its distance within 10.0 m?

Answer 1

Answer:

150000000000 m

0.0000005 seconds

33.33 ns

Explanation:

Speed of electromagnetic waves through vacuum = $3\times 10^8\ m/s$

Echo time = 1000 seconds

Echo time is the time taken to reach the object and come back to the observer

Distance = Speed×Time

$Distance=3\times 10^8\times \frac{1000}{2}=150000000000\ m$

Venus is 150000000000 m away from Earth

Time = Distance / Speed

$Time=\frac{75}{3\times 10^8}=0.00000025\ seconds$

Echo time will be twice the time

$Echo\ time=2\times 0.00000025=0.0000005\ seconds$

The echo time will be 0.0000005 seconds

Difference in time = Difference in distance / Speed

$\Delta t=\frac{\Delta d}{v}\\\Rightarrow \Delta t=\frac{10}{3\times 10^8}\\\Rightarrow \Delta=33.33\ ns$

The accuracy by which I will be able to measure the echo time is 33.33 ns