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Catching Football (Projectile Motion)

  1. Feb 24, 2013 #1
    1. The problem statement, all variables and given/known data

    In a football game, a quarterback passed a ball to a receiver while running at 1.5 m/s
    forward. The ball was released at a height of 2.5 meters with an angle of 45 degrees and
    an initial velocity of 20 m/s. The receiver ran from behind to catch the ball at a height of
    2 m.

    a) Find the range or distance traveled by the ball.

    b) Find the initial distance between the receiver and the quarterback, if the
    receiver ran at constant velocity of 7 m/s to catch the ball. Assume he
    started running at the same time as the ball was thrown.

    c) Find the final velocity of the ball and its direction.

    2. Relevant equations

    y=yo+voy*t + 1/2*a*t^(2)
    x=xo+vox*t

    Vb/e=Vb/q + Vq/e
    Vb/e= velocity of ball relative to the earth
    Vb/q= velocity of ball relative to quarterback
    Vb/e= velocity of quarterback relative to earth

    3. The attempt at a solution

    Vb/e-x= Vb/q-x + Vq/e-x
    Vb/e-x= 20cos(45) + 1.5= 15.64m/s

    Vb/e-y= Vb/q-y + Vq/e-y
    Vb/e-y = 20sn(45) + 0= 14.14m/s

    y=yo+voy*t + 1/2*a*t^(2)
    2=2.5 + 14.14*t - 4.905*t^(2)
    (quadratic formula)
    t= 3.20

    A) x= xo + vox*t
    x= 15.64*(3.2015)= 50.07m

    B) x= xo + vox*t
    50.07=xo +7*(3.2015)
    Xo = 27.6675m

    C) Vy= Voy*t +a*t
    Vy= 14.12 - 9.81(3.2015) = -17.28m/s

    Vb/e= 23.29m/s

    θ= -47.8 South of East

    Is my work correct? May be a little long but thanks for checking!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 24, 2013 #2

    rude man

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    It is not made clear whether the initial velocity of the ball was in the qb's reference frame or that of the stadium ...
     
  4. Feb 24, 2013 #3
    So what do we do?
     
  5. Feb 24, 2013 #4

    rude man

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    Ask the teacher what he meant. If it's a textbook question you can assume either case or work it both ways. Or ask your teacher what to assume.

    EDIT:
    I see you have already gotten the right equations. You've assumed the ball's initial v_x = 20cos(45) + 1.5 and I think this is the best assumption.

    Your work is excellent! I got all the same equations and numerical answers I checked (I did not check all your math, just some of it).
     
    Last edited: Feb 24, 2013
  6. Feb 25, 2013 #5
    Ok I will. I had a quick question though, if the ball's velocity was with respect to the earth would you just ignore the quarterback moving at 7m/s?
     
  7. Feb 26, 2013 #6

    rude man

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    Yes, which is why the fact that they gave you his speed suggested that they meant that speed to be added to his x throwing velocity.

    BTW I think his speed was 1.5 m/s. The fullback (or whoever) was running at 7.

    Good work!
     
  8. Feb 26, 2013 #7
    Thank you!!!!
     
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