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 (in m) is the planet Venus if the echo time is 900 s? m (b) What is the echo time (in µs) for a car 80.0 m from a Highway Patrol radar unit? µs (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 11.5 m? ns

a) 1.35 x 10^11 m

b) 0.53 µs

c) 8 ns

Explanation:

Radar involves the use of radio wave which has speed c = 3 x 10^8 m/s

a) for 900 s,

The distance for a round trip = v x t

==>  (3 x 10^8) x 900 =  2.7 x 10^11 m

The distance of Venus is half this round trip distance = (2.7 x 10^11)/2 = 1.35 x 10^11 m

b) for a 80.0 m distance of the car from the radar source, the radar will travel a total distance of

d = 2 x 80 = 160 m

the time taken = d/c = 160/(3 x 10^8) = 5.3 x 10^-7 s = 0.53 µs

c) accuracy in distance Δd = 11.5 m

Δt = accuracy in time = Δd/c = 11.5/(3 x 10^8) = 3.8 x 10^-8 = 38 ns

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