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Relative Velocity/Two-dimensional motion

  1. Feb 13, 2010 #1
    1. The problem statement, all variables and given/known data
    Suppose a Chinook salmon needs to jump a waterfall that is 1.50 m high. If the fish starts from a distance 1.18 m from the base of the ledge over which the waterfall flows, find the x- and y-components of the initial velocity the salmon would need to just reach the ledge at the top of its trajectory.


    2. Relevant equations
    x-component
    vx=v0*x + ax*t
    deltax=v0x*t+.5ax*t^2
    vx^2=v0x^2+2*ax*deltax

    also y-components, replace x components above

    v= (vx^2+vy^2)^.5 (pythagorean theorem)

    theta = tan^-1 (vy/vx)

    I don't know, since they're looking for the v0x and v0y, or the x- and y- components of velocity.

    3. The attempt at a solution
    Okay, I only managed to make a diagram, but otherwise, no luck.
     
  2. jcsd
  3. Feb 13, 2010 #2
    I think they are looking for the added vector of the v0x and the v0y.

    You are given the angle from the right triangle (with legs 1.5 and 1.18). You know you need to traverse at least 1.18 m before you reach 1.5 m in height (this can provide a time). And finally, you know the acceleration of gravity. The rest is grunt work.
     
  4. Feb 13, 2010 #3
    Yes, but I don't know which formulas to use. I just don't know how to find time. I have the formulas ready, but if all i have is the distance, but how can I find time, if I'm looking for velocity?
     
  5. Feb 13, 2010 #4
    For your problem there is only one formula, F = ma ?

    F_x = ma_x = 0 --> v_x = v_ox --> x = x_o + v_ox*t
    F_y = ma_y = -mg -->

    v_y = v_oy - g*t --> y = y_o + v_oy*t - g*t^2/2
     
  6. Feb 13, 2010 #5
    I don't think force has anything to do with it.
     
  7. Feb 13, 2010 #6
    There is no force in the x direction so when the fish "leaps" it will move in the x direction with constant velocity. In the y direction the fish moves with some initial velocity in the y direction but this velocity changes with time as the force of gravity acts on the fish.

    Parabolic motion, assume the velocity of the fish in the y direction goes to zero when the fish reaches the ledge.
     
  8. Feb 13, 2010 #7
    The time can be found with the acceleration of gravity and v0y as the initial velocity in the y direction.
     
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