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Momentum Question: Asteroid Collision

  1. May 8, 2013 #1
    1. The problem statement, all variables and given/known data

    Asteroid A is travelling at 40.0m/s and collides with asteroid B which is at rest. Both asteroids have the same mass, but asteroid A deflects off of its path by 30.0° above the horizontal, and asteroid B begins to travel 45.0° below the horizontal. What is the speed of asteroid A?

    2. Relevant equations

    PA1X = PA2X + PB2X

    PA1X = 40.0m/s*mA

    PA2X = mA*VA2*cos30°

    PB2X = mB*VB2*cos45°

    PA2Y = mA*VA2*sin30°

    PB2Y = mB*VB2*sin45°

    3. The attempt at a solution

    Equation #1 mB*VB2*sin45° = mA*VA2*sin30°
    Equation #2 mB*VB2*cos45° + mA*VA2*cos30° = 40.0m/s*mA

    I isolate mB*VB2 from Equation #1 and get mB*VB2 = (mA*VA2*sin30°)/(sin45).

    Now I substitute mB*VB2 into Equation #2, and get (cos45°*VA2*sin30°)/(sin45°) + VA2*cos30° = 40.0m/s, I cancelled out mA.

    Next I isolate VA2*(sin30°)/(tan45°) + cos30° = 40.0m/s

    Finally VA2 = 78.2679m/s which is impossible because it shouldn't go faster after the collision. Also, my textbook's answer is 23.3m/s.
     
  2. jcsd
  3. May 8, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    Careful... didn't VA2 multiply both terms on the left?
    Yup, 78 m/s is definitely too large. It's also possible that your textbook's answer is not correct :wink:
     
  4. May 8, 2013 #3
    You're right - thank-you so much!
     
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