Question

1 – Consider the car-caravan analogy. In this problem, assume a propagation speed of 70 km/hr and that each toll booth takes 6 seconds to service a car. Suppose the caravan of 10 cars begins immediately in front of the first toll booth, travels 50 km to a second toll booth, then another 50 km to a third toll booth, and finally stops immediately after the third tool booth. Thus, they travel a total of 100 km. What is the total end-to-end delay? Where is the last car in the caravan after one hour? Your answer must include a distance/specific location, and not only a relative direction.

Answer 1

`Hey,

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a.)

The cars start at front of first toll booth and ends after the third toll booth.

Transmission delay or d_trans at toll booth = 6 seconds at each toll booth for each car.

There are 10 cars. So total transmission delay at each toll booth = 60 seconds = 1 minutes.

Propagation delay or d_prop = distance travelled / propagation speed

Total distance = 100 km.

d_prop = 100 km/ 70 kmh = (100/70) * 60 minutes = 85.71.

Total end to end delay = d_prop + (time taken at each of the three toll booths)

= d_prop + 3 * d_trans (because there are 3 booths)

= 85.71 + 1*3 = 88.71 minutes.

b.)

The last car in the caravan leaves the first toll booth after 60 seconds or 1 minutes. Therefore, the distance of the last car from the first toll booth after 60 minutes will be equal to distance travelled by it in (60 - 1) or 59 minutes

59 minutes = (59/60) hours.

Distance travelled = speed * time

= 70 km/hour * (59/60) hours

= 68.83 km.

Hence the last car will be 68.83 kilometers away from the first toll booth.

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