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Conservation of energy, ball kicked into a canyon

  1. Jan 4, 2010 #1
    1. The problem statement, all variables and given/known data
    A ball is ikicked off a 100.0 m canyon at an angle of 30.0 degrees above the horizontal with a velocity of 24.0 m/s. What maximum height does it reach above the canyon floor?


    2. Relevant equations
    WNC = KE + PE


    3. The attempt at a solution
    WNC = 1/2mvf^2 - 1/2mvi^2 + mghf - mghi
    1/2mvi^2 + mghi = 1/2mvf^2 + mghf

    I'm not sure what to do with the 30.0 degree angle?
     
    Last edited: Jan 4, 2010
  2. jcsd
  3. Jan 4, 2010 #2
    You can find the horizontal and vertical component of the initial speed of the ball
    with the angle. When the ball is at its highest point, the vertical component will be 0.
     
  4. Jan 4, 2010 #3

    PhanthomJay

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    You meant to say W_nc= delta KE + delta PE = 0, which is what you ended up with. When the ball reaches its max height, what is v_fy and what is v_fx?
     
  5. Jan 4, 2010 #4
    okay so after i have vix = 20.785 and viy = 12, what do i do with those?
     
  6. Jan 4, 2010 #5
    This is a projectile motion above a canyon. You've seem to have already found the vertical and horizontal components of the initial velocity so lets think about this some more.

    In a projectile motion we're eventually going to reach a peak right?

    Is there any specific property which notifies us that we've reached the peak of our projectile motion? (HINT: using the vertical/horizontal components of velcoity)
     
  7. Jan 4, 2010 #6
    the velocity in the y direction will equal 0.
     
  8. Jan 4, 2010 #7
    so i put that into the conservation of energy formula and solve for final height! thanks!
     
  9. Jan 4, 2010 #8
    I'm not entirely sure if that's correct. You told me above that the vertical component of its velocity will be 0 when it reaches its maximum height during its projectile motion. Calcuate this height and add it to the height of the ball initially above the canyon.

    That will give you its maximum height.
     
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