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Collision of baseball with falling person

  1. Jan 23, 2014 #1
    1. The problem statement, all variables and given/known data

    You throw a baseball at a 45 degrees angle to the horizontal, aiming at a friend who's sitting in a tree a distance, h, above ground. At the instant you throw your ball, your friend drops another ball.

    a) Show that the two balls will collide, no matter what your ball's initial speed, provided it's greater than some minimum value.
    b) Find an expression for that minimum speed.


    3. The attempt at a solution

    Am I expected to provided an arbitrary initial velocity value and time, t at collision and use it to prove that the collision will occur?
     
    Last edited: Jan 23, 2014
  2. jcsd
  3. Jan 23, 2014 #2
    You throw the ball by aiming it directly at your friend, as if gravity is not going to change its trajectory. If he is sitting a distance h above the ground, how far away from you horizontally is he (in terms of h)? If the initial velocity of your ball is v0, can you determine the trajectory of your ball (x and y as functions of time). If he drops his ball with an initial velocity of zero, can you calculate the x and y locations of his ball as functions of time? Can you determine if the two trajectories meet at any time?

    Chet
     
  4. Jan 23, 2014 #3
    Solved for part(a)
     
    Last edited: Jan 23, 2014
  5. Jan 23, 2014 #4
    I have solved for part(a)
    View attachment 65945


    How should I approach part (b)?
     
    Last edited: Jan 23, 2014
  6. Jan 23, 2014 #5
    For part b, you just have to make sure that the collision occurs above ground.
     
  7. Jan 23, 2014 #6
    Capture.JPG

    The above is my answer for part(a)

    I understand. But what is the initial premise from which I must work on?

    Edit: I'll try working on the assumption that at t = x/vicos45, the position of my ball must be y >0m
     
    Last edited: Jan 23, 2014
  8. Jan 23, 2014 #7
    Part(b):

    vi > SQRT(gx)
     
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