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Relative Motion Question Involving Rain and Moving Car

  1. Apr 1, 2009 #1
    1. The problem statement, all variables and given/known data
    A car travels due east with a speed of 45.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 45.0° with the vertical. Find the velocity of the rain with respect to the following reference frames.
    (a) the car

    (b) the Earth


    2. Relevant equations
    n/a


    3. The attempt at a solution
    I managed to find the answer of part a) which is 17.7 m/s using simple trigonometry although I didn't really understand why the sign was positive.
    I found the velocity of the car to be 12.5 m/s and with my diagram got:
    sin45=12.5/Vr (Vr= velocity of rain relative to the car)
    Vr = 12.7 m/s

    For part b, I thought that
    velocity of rain relative to car = velocity of car relative to earth - velocity of rain relative to earth
    So, 17.7 = Vre -12.5
    So I found the velocity of rain relative to the earth to be 30.2 m/s.

    I can't remember where I got that reasoning for part b from, but is that the only thing that's wrong?

    Please help...
     
  2. jcsd
  3. Apr 2, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    The sign just depends on your coordinate system; all they want is the magnitude of the velocity.
    OK.
    ?? Typo?

    Not exactly. Instead:
    velocity of rain relative to car + velocity of car relative to earth = velocity of rain relative to earth
    No. Realize that the equation above is a vector equation. Apply it to each component separately.
     
  4. Apr 3, 2009 #3
    So, when you say apply the vector equation to each component separately, can I split say the vector of velocity of rain relative to car into horizontal and vertical components?

    And that would mean that
    horizontally: Vre= -12.5 +12.5 = 0
    vertically: vre =12.5 + 0 = 12.5

    So answer is just 12.5 m/s (down)

    If that's not right, then I'm not sure what you mean...
     
  5. Apr 3, 2009 #4

    Doc Al

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    Staff: Mentor

    You got it.
     
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