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Homework Help: Time dilation and a car

  1. Aug 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Now, suppose the student wishes to bring back some ice cream from the restaurant for her friends at school, but since it is such a hot day, the ice cream will melt away in the car in only 5 minutes. How fast will the student have to drive back to get the ice cream to her friends before it completely melts?

    C=40mph(for these problems)
    Time=5 minutes
    Distance=7.5 miles

    2. Relevant equations
    Dt= change in time
    p= proper interval
    Dt-p= d/v

    Dt-p=Dt/lambda or dt/sqrt(1-v^2/c^2)

    3. The attempt at a solution


    .1875=(5minutes/60minutes per hour)/sqrt(1-v^2/40^2)

    rearranging it becomes:

    v=sqrt( -((.083hr/.1875hr)^2-1)*40^2)

    answer I get is 35.8mph

    The online homework tells me I am wrong either by sig figs or by bad rounding.
  2. jcsd
  3. Aug 5, 2009 #2


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    Homework Helper

    Well then, don't round until you get to the final answer, and try out different numbers of sig figs. Have you tried 36 mph?
  4. Aug 5, 2009 #3
    I have tried 36, 35.8,35.83

    I went back and put 37 and it said I was correct, the correct answer was actually 36.6. I haven't the faintest clue as to how it is 36.6 mph.
    Last edited: Aug 5, 2009
  5. Aug 6, 2009 #4


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    Science Advisor
    Homework Helper
    Gold Member

    Yes, the correct answer is 36.55 mph. The problem is not with the number crunching but with the set-up of the equations. The correct time interval for fetching the ice-cream in the Earth's frame is 7.5/v not 7.5/40. The student does not travel at the speed of "light."
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