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2-D car collision, finding speed and angle

  1. Jun 21, 2010 #1
    1. A 1000- kg car collides with a 1200- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 25.0 km/h in a direction of 20 o with respect to the positive x axis. The heavier car moves at 28 km/h at -44 o with respect to the positive x axis.
    What was the initial speed of the lighter car (in km/h)? What was the initial direction (as measured counterclockwise from the x-axis)?




    2. x-momentum= m1v1cos(angle1) + m2v2cos(angle2)
    y-momentum= m1v1sin(angle1) + m2v2sin(angle2)
    magnitude momentum= sqrt(Xtotal)^2 + (Ytotal)^2
    = sqrt((m1v1cos(angle1) + m2v2cos(angle2))^2 + ((m1v1sin(angle1) + m2v2sin(angle2))^2




    3. By plugging into this equation, I come up with 49602.6 m/s, but it's not right. I need to get the velocity correct before I can make an attempt to find the initial direction
     
  2. jcsd
  3. Jun 21, 2010 #2
    Firstly you need to use law of conservation of momentum for xaxis.
    Then use for yaxis. Don't mix two axes. Two equations , two unknowns so you can find the correct answer.
     
  4. Jun 21, 2010 #3

    collinsmark

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    Your relevant equations seem correct, but show us your work, and maybe we can help you find out what went wrong. You're correct that 49602.9 m/s isn't right. 49602.9 m/s is greater than Earth's escape velocity.
     
  5. Jun 21, 2010 #4
    I will call the car with mass of 1000Kg car A, the other one car B. Applying conservation of momentum in the x and y directions we have:
    mAVAx=mAVA'x + mBVB'x for the x-direction
    we know all the masses and velocities after collision, therefore we can solve for VA which is the magnitude of the velocity in the x-direction. Following the same concept for the y-direction, I obtained magnitude of VA 50Km/h with an angle of -17.25 degrees from the x-axis. Someone confirm this.
     
  6. Jun 22, 2010 #5
    Thank you all for your input! I was able to get the answer by splitting into the 2 equations like everybody said to do. 49.9 km/hr and 342.8 deg were the answers I came up with. Thanks again!
     
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