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Finding initial velocity of a cat jumping through a hoop

  1. Sep 21, 2016 #1
    1. The problem statement, all variables and given/known data
    Kit the cat is going to jump through a hoop. He begins on a wicker cabinet at a height of 1.745 m above the floor and jumps through the center of a vertical hoop, reaching a peak height 3.115 m above the floor.

    With what initial velocity did Kit leave the cabinet if the hoop is at a horizontal distance of 1.567 m from the cabinet? (Express your answer in vector form)

    2. Relevant equations
    X (or Y) = vit + 1/2at2
    Vf2 = Vi2 + 2a(x2-x1)
    And possibly quadratic equation.

    3. The attempt at a solution
    I was able to calculate the initial velocity of the y direction using Vf2 = Vi2 + 2a(x2-x1) (I know because the cat reaches peak height at 0, the vertical velocity at that time was 0).From there, I tried to solve for t. I know once I get t, I can find the initial velocity of x, but I came to an error in what I believe is my t. I tried plugging into Y = vit + 1/2at2 and made it into the quadratic formula, but got two positive answers 0.54739930925614 s and 0.51076395604999 s. Then I tried the Vf = Vi + at and got .529 s.
    What can I do to find time, correctly?
     
  2. jcsd
  3. Sep 21, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    Your final method works fine. t = 0.529 s looks good.

    Your other method would have worked, too if you had included the initial height. That is, the more complete version of the kinematic equation you used is:

    ##y(t) = y_o + v_o t + \frac{1}{2} a t^2##

    Note the ##y_o## term representing the initial offset ("launch height" in this case).
     
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