1-Consider the car-caravan analogy from Section 4 in Chapter 1. In this problem,
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Question
1-Consider the car-caravan analogy from Section 4 in Chapter 1. In this problem, assume a propagation speed of 60 km/hr and that each toll booth takes 12 seconds to service a car. a) (7 points) Suppose the caravan of 10 cars begins immediately in front of the first toll booth, travels 40 km to a second toll booth, then another 40 km to a third toll booth, and finally stops immediately after the third tool booth. Thus, they travel a total of 80 km. What is the total end- to-end delay? b) (3 points) Where is the last car in the caravan after 30 minutes? Your answer must include a distance/specific location, and not only a relative direction.Explanation / Answer
a.)
The cars start at front of first toll booth and ends after the third toll booth.
Transmission delay or dtrans at toll booth = 12 seconds at each toll booth for each car.
There are 10 cars. So total transmission delay at each toll booth = 120 seconds = 2 minutes.
Propagation delay or dprop = distance travelled / propagation speed
Total distance = 80 km.
dprop = 80 km/ 60 kmh = (80/60) * 60 minutes = 80 minutes.
Total end to end delay = dprop + (time taken at each of the three toll booths)
= dprop + 3 * dtrans (because there are 3 booths)
= 80 + 2*3 = 86 minutes.
b.)
The last car in the caravan leaves the first toll booth after 120 seconds or 2 minutes. Therefore, the distance of the last car from the first toll booth after 30 minutes will be equal to distance travelled by it in (30 - 2) or 28 minutes
28 minutes = (28/60) hours.
Distance travelled = speed * time
= 60 km/hour * (28/60) hours
= 28 km.
Hence the last car will be 28 kilometers away from the first toll booth.
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