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Change in momentum help

  1. Oct 13, 2006 #1
    A baseball pitcher delivers a fastball that crosses the plate with an angle of 5.67 degrees relative to the horizontal and a speed of 80.1 miles/hour. The ball (mass 0.145 kg) is hit back over the head of the pitcher at an angle of 37.09 degrees with respect to the horizontal and a speed of 108.5 miles/hour. What is the magnitude of the impulse received by the bat?

    Ok, impulse is the change in momentum.
    But since the mass is pitched at an angle and is hit at an angle you need to decompose the velocity vector into it's y and x components.

    vyi=(35.81)sin(180-5.67)=3.54 m/s
    vxi=(35.81)cos(180-5.67)=-35.63 m/s

    vyf=(48.50)sin(37.09)=29.25 m/s
    vxf=(48.50)cos(37.09)=6.78 m/s

    Add the x and y components to each other
    y's=25.71 m/s
    x's=42.41 m/s

    Then find the velocity of the summed vectors
    vf=sqr(vx^2+vy^2)=49.6 m/s

    p=mv=(0.145 kg)(49.6 m/s)=7.192 kg m/s

    When I enter this into my homework site for my class, it tells me this is the wrong answer. I'm I missing something here? At first I thought maybe I'm not suppose to find the difference between 180 and my angles for the intial velocties. So I tried it just with the original angles and I still get a wrong answer message. Please help.

  2. jcsd
  3. Oct 14, 2006 #2


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    Hmm, I know very little about baseball (I'm a brit) but when that fastball is crossing the plate, is that the pitcher's plate,or the home plate ??
  4. Oct 14, 2006 #3
    Home plate
  5. Oct 15, 2006 #4


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    that should be 38.69

    you subtracted instead of adding here.
  6. Oct 15, 2006 #5
    What is the correct anwer, because I fixed the mistakes and I'm still getting a wrong answer message. Right now I have 29.25+3.54 for the y's because the vectors are going in the same direction. For the x's I have 38.69-35.63 because the vectors are going in opposite directions. I get 4.77 kg m/s for the impulse. Is this right?
  7. Oct 15, 2006 #6


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    You've been subtracting the x's instead of adding them.
    Before impact, the ball has a speed of 35.63 m/s to the right (going by your diagram)
    After impact, the ball has a speed of 38.69 m/s to the left (going by your diagram)
    So the overall change in velocity (which is a vector) is the sum of the speeds = 74.32 m/s.

    Edit: I get 11.78 kg m/s as the change in momemtum.
    Last edited: Oct 15, 2006
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