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Upper lower bound question

  1. Apr 10, 2007 #1
    1. The problem statement, all variables and given/known data
    Martin won the 400 metre race in a time of 1 minute
    The time was correct to a tenth of a second
    The distance was correct to 1cm

    Find the upper and lower bounds of Martin's speed in km/h

    2. Relevant equations
    Speed = distance over time


    3. The attempt at a solution
    400 = 0.4km to 1 cm it's 0.4005 or 0.3995
    1 second = 0.00277777777777 hours

    how do I find the upper and lower bounds for a tenth of a second from the number above (it's recurring).

    THe upper bound of speed = upper bound of distance/lower bound of time
    The lower bound of speed = lower bound of distance/upper bound of time

    Thanks
    :cool:
     
  2. jcsd
  3. Apr 10, 2007 #2

    HallsofIvy

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    You've misplaced a decimal position. If the distance is "correct to the nearest cm"- i.e. rounded to the nearest centimeter, then it could be as much as 400 m+ .5 cm= 400 m+ .005 m= 400005 m = .400005 km. Similarly, if could be as low as 400m- .005 m= 399.995 m= .499995 km.

    For the "nearest tenth of a second", the true time could be as low as 1 min+ .5 second= 1 min+ .008333 min= 1.008333 min= 0.0168055 hr or as low as 1 min- .5 second= 1 min- .008333 min= .99166 min= .016528 hr.

    You don't need to get an exact value do you?
    "The upper bound of speed = upper bound of distance/lower bound of time"
    so .400005 km/.016528 hr= 24.20 km/hr
    "The lower bound of speed = lower bound of distance/upper bound of time"
    so .499995 km/0.0168055 hr = 29.75 km/hr.

    If you do need the exact value then leave the numbers in fraction form.
    The maximum distance is 400.005 m= 0.400005= 400005/1000000 km and the minimum distance is .49995= 499995/1000000 km.
    The minimum time is 1- (1/2)/60= 1- 1/120= 119/120 min= 119/7200 hr and the maximum time is 1+ (1/2)/60= 1+ 1/120= 121/120 minutes= 121/7200 hr.

    The upper bound on speed is (400005/1000000)(7200/119)= 2880036/11900000 km/hr while the lower bound on speed is (499995/1000000)(7200/121)= 3599964/12100000 km/hr. Those, of course, can be reduced.
     
  4. Apr 10, 2007 #3
    The actual question is:

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  5. Apr 11, 2007 #4
    you've made a mistake :bugeye:

    Code (Text):
    You don't need to get an exact value do you?
    "The upper bound of speed = upper bound of distance/lower bound of time"
    so .400005 km/.016528 hr= 24.20 km/hr
    "The lower bound of speed = lower bound of distance/upper bound of time"
    so [COLOR="Red"].499995 [/COLOR]km/0.0168055 hr = 29.75 km/hr.
    isn't it .399995 = 23.801km/h

    and isn't the upper bound

    .400005 / 0.016805555 = 23.802km/h

    both answers are to 5.s.f
     
  6. Apr 11, 2007 #5

    HallsofIvy

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    Yes, of course! Thank you.
     
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