Question 2. Problem 3 on page 73 (10 points) Consider the car-caravan analogy we

Question

Question 2. Problem 3 on page 73 (10 points) Consider the car-caravan analogy we discussed in the class. The cars propagate at 100km/hr. A tollbooth services a car at a rate of one car every 12 seconds. km7 75 km ten-car toll booth toll booth toll booth caravan Answer the following with brief explanatiorn When these ten cars line up in front of the first toll booth, how long it takes for them to finishing just after the third toll booth shown in the figure above (Note: ten cars will line up in front ofa toll booth before any car goes through the toll booth)? Repeat (a), now assuming there are eight cars in the caravan instead of ten. a. b.

Explanation / Answer

Propagation Speed = 100km/hr

Distance between two toll booths = 75km

Toll booth service time = 12seconds

a)

Propagation delay or dprop = Total distance travelled / propagation speed

dprop = 150km / 100kmph = 1.5hrs = 90 minutes

Service time at one toll booth dtrans = 12 seconds = 0.2 mins

for all cars dtrans = 0.2x10 = 2mins

dtrans for all booths for all cars = 2mins x 3 = 6mins

Total delay = dprop + dtrans = 90 + 6 = 96minutes

b)

8 cars instead of 10

dprop = Total distance / propagation speed = 150km / 100kmph = 1.5hrs = 90 minutes

dtrans at one toll = 12seconds = 0.2 mins

dtrans at all tolls for all cars = 0.2 x 8 x 3 = 4.8 mins

Total delay = 90 + 4.8 = 94.8 minutes

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