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Momentum, vector addition question

  1. May 1, 2016 #1
    1. The problem statement, all variables and given/known data
    A car with a mass of 1400 kg is westbound at 50 km/h. It collides at an intersection with a northbound truck having a mass of 2000 kg and traveling at 40 km/h. What is the initial common velocity of the car and trucks after collision if it's an inelastic collision?

    2. Relevant equations
    p = mv

    3. The attempt at a solution
    So I got this question wrong, but I can't seem to get the right answer no matter how I look at it. I think maybe I lost marks because I didn't use the method the teacher wanted (which is fine with me)?? Let me know guys.

    m1v1 + m2v2 = (m1 + m2)vf

    (1400kg)(13.888m/s) + 0 = (1400kg + 2000kg)(vfx)
    vf = 5.7189... m/s

    0 + (2000 kg)(12.5 m/s) = (1400kg + 2000kg)(vfy)
    vf = 7.35294.. m/s

    (5.7)2 + (7.3)2 = r2
    vf = 9.3 m/s

    tan-1(7.3 / 5.7 m/s)
    = 52 N of W
    = 128 degrees

    I tried a different approach and found P(car) and P(truck), then P(combined), solved for Vf, but I got the same answer:

    (1400 kg)(13.888 m/s) = 19443.2 kg m/s West
    (2000 kg)(12.5 m/s) = 25000 kg m/s North
    pythagorean theorem...
    = 31670.77559 kg m/s
    momentum is conserved so
    31670.78 = (2000 + 1400) vf
    vf = 9.3 m/s!!
     
  2. jcsd
  3. May 1, 2016 #2

    NascentOxygen

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    Staff: Mentor

    Hi. smiley_sign_welcome.gif

    Your method looks right, though I haven't checked your arithmetic.
     
  4. May 1, 2016 #3

    Simon Bridge

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    Your method is correct - your answer is different from mine.
    Note: do algebra before plugging numbers in, check for rounding errors.
     
  5. May 1, 2016 #4
    Hey, redid the algebra, got the same answer. What was your answer Simon Bridge?


    vfx = (1400 kg)(13.888m/s) / (1400kg + 2000kg)
    =5.7189 m/s
    vfy = (2000 kg)(12.5 m/s) / (1400kg + 2000kg)
    = 7.35294 m/s

    (5.71892 + 7.352942)1/2 = vf
     
  6. May 1, 2016 #5
    Never mind, I converted 40km/hr to 12.5 m/s, should have been 11.1 m/s. That sucks, lost a lot of marks for it.

    I got 8.7 m/s as my answer.
     
  7. May 2, 2016 #6

    Simon Bridge

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    ... and that was my answer.
    I did the components in kmph and converted at the end... the fewer conversions you do the better.
     
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