Radar is often used to determine distances to various objects by measuring the d

Question

Radar is often used to determine distances to various objects by measuring the delay time for the echo of an electromagnetic pulse from the object.   

Part (a)  How far away, in meters, is the planet Venus if the echo delay time is 985 s?   

Part (b)  What is the echo delay time, in microseconds, for a car 77.5 m from a Highway Police radar unit?   

Part (c)  To what precision, in nanoseconds, must you be able to measure the echo time to an airplane 15 km away to determine its distance within 10.5 m?

Explanation / Answer

Part (a) We know that in case of a Radar, Distance R to the reflecting object can be obtained by following relation:

R = (Speed of light * Delay time)/2

= (3*10^8)*(985)/2

=147750000000 metres Answer

Part (b) We also know that, Echo delay time is obtained by following relation

Echo delay time = (2*Distance of reflecting object)/Speed of light

= (2*77.5)/(3*10^8)

= 51.6 * 10^-8 seconds

= 516 Nanoseconds Answer

Part (c) Accuracy in eco time measurement is given by following relation:

Eco time = (2*Distance)/Speed of light

= (2*10.5)/(3*10^8)

= 7*10^-8 seconds

= 70 Nano seconds Answer

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