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Homework Help: Rewriting the constant

  1. Mar 12, 2010 #1
    Ok, here is a certain formula and I have to change it.

    V = 5.47[tex]\sqrt{h}[/tex]

    V is velocity in mph while h is distance in ft.

    I need to determine a new constant so that V is in feet per second. How do I go about doing that? Do I just convert V first and then take the constant and multiply it by the numbers that I needed to convert to ft/s?

    By the way, h stays the same as just ft.
  2. jcsd
  3. Mar 12, 2010 #2


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    If 1 mph is 1.67 ft/s (recheck this for me)

    How much ft/s is V mph?

    EDIT: As Char. Limit says, 1mph is 1.467 ft/s

    I forgot a 4 it seems.
    Last edited: Mar 12, 2010
  4. Mar 12, 2010 #3

    Char. Limit

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    1 mph is not 1.67 ft/s.

    1 mph is 1.467 ft/s
  5. Mar 13, 2010 #4


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    There are 5280 ft/mi. There are 60 sec per minute and 60 minutes per hour and so 3600 seconds per hour.

    1 mi/hr= (1 mi/hr)(5280 ft/mi)/(60 sec/hr)= 5280/60 (mi/hr)(ft/mi)(hr/sec= 1.47 ft/sec.
  6. Mar 13, 2010 #5


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    And there are 1000 metres / kilometre

    I dunno... metric units just seem simpler...
  7. Mar 13, 2010 #6
    Yeah I know how to convert but I'm asking how do I change the constant 5.47 in the formula to accommodate V in ft/sec? Do I just multiply 5.47 by the numbers that I multiplied into V to convert it?
  8. Mar 13, 2010 #7
    I believe you would just multiply the equation the same way HallsofIvy has done; it's called the Grid Method.
  9. Mar 13, 2010 #8


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    Just put the units in explicitly:

    [tex]v=5.47 \frac{\mbox{miles}}{\mbox{hr ft}^{1/2}}\sqrt{h}[/tex]

    and convert the units on the constant like you normally do.
  10. Mar 13, 2010 #9
    I have no idea how you got that unit for the constant.

    I also don't know what you mean by converting the units on the constant like you normally would. Convert the units on the constant into what?
  11. Mar 13, 2010 #10


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    The units of [itex]\sqrt{h}[/itex], if h is in feet, is ft1/2, which cancels with the ft1/2 in the denominator of the units of the constant. The units of v is mph, so the what's left over after the ft1/2 cancels must be miles/hr.

    If you want the formula to give an answer in ft/s, the constant needs to have units of ft/(s ft1/2).
  12. Mar 14, 2010 #11
    I got 8.02 as the new constant. Is that right?
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