F.2 Approximation and Errors

用戶72904

2007-02-20 7:43 pm

1. Wesley participated in a touring car race where the participants have to complete 200 laps of the race track. The length of the inner lane of the race track is 2 km and that of the outer lane is 2.125 km. Wesley took around 31 minutes 40 seconds to complete the first 50 laps of the race track.
a) Estimate the time taken for Wesley to complete the whole race.
b) Estimate the distance travelled by Wesley for the whole race.
c) Estimate the average speed of Wesley throughout the whole race.

回答 (1)

taolo

2007-02-20 10:06 pm

✔ 最佳答案

1. As approximation approach, we should assume Wesley will took the same time to complete same distance.
So, complete 50 laps use 31 minutes 40 seconds,
complete 50 laps use: 4*31 minutes 40 seconds=124 minutes 160 seconds
=126 minutes 40 seconds
=2 hours 6 minutes 40 seconds

2. We should assume the length of the touring car travelled is the mean value of 2km and 2.125km
So the lap length assumed to be (2+2.125)/2=2.0625km
So total distance travelled by Wesley for the whole race=2.0625*200=412.5km

3. estimated speed= estimated distance/estimated time
estimated speed= 412.5km/2 hours 6 minutes 40 seconds
= 412.5km/2 + 6/60 + 40/3600 hours
=412.5/2.111
=195.4km/h

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