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Projectile Motion given 2 position equation

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    The motion of a human body through space can be precisely modeled as the motion of a particle at the body's center of mass. The components of the displacement of an athlete's center of mass from the beginning to the end of a certain jump are described by the two equations below, where t is the time at which the athlete lands after taking off at time t = 0.

    xf =0 + (11.1 m/s)(cos 20.3°)t
    0.369 m = 0.812 m + (11.1 m/s)(sin 20.3°)t - 1/2(9.80 m/s2)t2

    2. Relevant equations
    (a) Identify his position.
    ? meters ihat + ? meters jhat
    (b) Identify his vector velocity at the takeoff point.
    ? m/s at ? ° above horizontal
    (c) The world long jump record is 8.95 m. How far did the athlete in this problem jump?
    ? m

    3. The attempt at a solution
    So, I drew out a diagram and it seemed to make sense to me but the answers were wrong. for a) i got you would just take the component vectors, so Vxi= (11.1 m/s)(cos 20.3) and Vyi= (11.1 m/s) (sin20.3). But that was wrong. I got b). and for c) i thot you could jus pick out the information and it would be .369 but then realized that is only in the y direction, but time isnt give, so how are we supposed to find the x_final?
     
  2. jcsd
  3. Oct 16, 2008 #2

    LowlyPion

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    Homework Helper

    For a) you identified his components of velocity as his position.
    But the question asked about the Position P(t) in terms of the unit vectors.

    For c) you have two equations in t. Once you solve for t, you can determine x.
     
  4. Oct 17, 2008 #3
    all right, i got the t and solved c.

    however, for a) im still a bit confused. are they asking for his initial position? becuase if they are wouldnt it be 0 for ihat and .443 jhat? i got the 0 ihat correct, but the.443 was wrong?
     
  5. Oct 17, 2008 #4

    LowlyPion

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    I'm going to say that I think it is worded poorly. If it is initial position that is asked for, then it will be the x=0 and y=.812 at t=0 The final position is a consequence of his jump and as far as initial position is concerned is not a factor.

    My initial reading of the question suggested to me they wanted the unit vectors as a function of the time. But if x=0 is the coefficient of i-hat then I suppose initial condition is what they asked. But I am not entirely happy with that interpretation.
     
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