SOMEONE HAS ANSWERED A-D, BUT DID NOT DO E OR F. IF YOU COULD EXPLAIN E AND F, T
ID: 1885635 • Letter: S
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SOMEONE HAS ANSWERED A-D, BUT DID NOT DO E OR F. IF YOU COULD EXPLAIN E AND F, THAT WOULD BE EXTREMELY HELPFUL
You set out from town A and head east to town B 120 km away. Your vehicle has an odometer that is not particularly accurate (it could be off by 1–2 km, or more, after driving 50 km). You carry a decent watch, which is great at keeping time over short intervals, but it has been months since you last reset it. In other words, you can measure time intervals accurately, but do not know exactly what time it is. A short time into your journey, your car breaks down.
(a) According to your odometer, you have traveled 56 km. Estimate your position.
(b) As you push your car to the shoulder of the road, a red bus zooms by heading from A to B. You glance at your watch and notice that it is exactly 21 minutes past the hour. You know that the red buses are prompt, and they leave town A every hour on the hour traveling at exactly 3 km/min. Can you estimate your position without using the odometer information?
(c) Estimate your position and clock bias based on all the information so far. (Hint: Write two equations that relate your position and clock bias to the available information. These equations are sometimes referred to as navigation equations.)
(d) At 25 minutes past the hour by your watch, you observe a blue bus zoom past at 2.5 km/min, going from B to A. Blue buses leave town B every hour on the hour promptly and drive to town A at a constant speed. Estimate your position and clock bias based on all the information so far. (Hint: Recall that your watch can measure time intervals accurately.)
(e) How would your solution be affected if your watch were exactly five minutes faster and all the clocks in town A and town B were running five minutes fast?
(f) Now suppose that your odometer never worked and the only vehicles you see are the identical yellow cabs of carrier L1. These cabs leave town A every minute on the minute and travel at exactly 1 km/min to town B. Can you estimate your position and clock error? Would it help if there were identical green cabs of carrier L2 leaving town B every minute on the minute and traveling at 1 km/min to town A? Explain briefly.
Explanation / Answer
e)
If all the clocks and the watch were running 5 min faster, that means they will tell same exact time so red bus would have taken exactly 21 minutes to reach the position.
So your exact position would be = 3 Km/min x 21 minutes = 63 Km.
f)
In this case, since yellow cabs are operating 1 cab per minute, so if clock is running correctly, then you would have seen 21 cabs on the road, either you were overtaking them or they are passing you. If your watch is running faster, that means you would have seen fewer cabs than 21. Or if your watch was slower, then there would have been more than 21 yellow cabs that you would have seen. The difference in number of yellow cabs from 21 will be the error in the watch in minutes, as they are running each minute. So, the position can be calculated by adjusting the watch time.
Same principle can be used in counting green cabs in those 21 minutes on your watch. If more than 21 green cabs encountered on the way, the watch is running slow. And if less than 21 green cabs encountered, watch is running fast. So not much help over yellow cabs.
Hope this explains.
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