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Minimum Velocity only given distance

  1. Sep 13, 2008 #1
    Minimum Velocity only given distance!!

    1. The problem statement, all variables and given/known data
    A soccer ball is kicked by a goalie to a position that is 65 meters down field. What is the minimum velocity necessary to achieve this feat?


    2. Relevant equations
    v2=vf2+2a(x-xo)


    3. The attempt at a solution
    v2=02+2a(65m)
     
  2. jcsd
  3. Sep 13, 2008 #2
    Re: Minimum Velocity only given distance!!

    Assuming no air resistance, the velocity required will be a minimum what the launch angle is 45 degrees above the horizontal. Use the range equation.
     
  4. Sep 13, 2008 #3
    Re: Minimum Velocity only given distance!!

    But no degree angle is specified, does it still have to be 45 degrees? you can still kick a ball and have it roll horizontally
     
  5. Sep 13, 2008 #4
    Re: Minimum Velocity only given distance!!

    True; I thik the statement of the problem implies that the ball is kicked at some angle above the horzontal and when it returns to the ground, it has convered a horizontal distance of 65m.
     
  6. Sep 13, 2008 #5
    Re: Minimum Velocity only given distance!!

    But to use an angle you need an initial velocity, no? None is specified. My professor said that this problem was very difficult and had a trick to it. There's a part b) that says "if it was kicked at 50 degrees instead" where would the ball land?
    that might be the clue, so perhaps there's an implied angle?
     
  7. Sep 13, 2008 #6
    Re: Minimum Velocity only given distance!!

    Well, how about this. The range equation is

    R = [tex]\frac{V_{0}^{2} sin 2\theta}{g}[/tex]

    If you solve the equation for Vo and differentiate the result with respect to theta (dVo / dtheta), set it equal to zero and solve for theta, you get 45 degrees. That proves that the min speed for a given range occurs when theta is 45 degrees.

    If you then solve the range equation for Vo and substitute 45 degrees,

    ([tex]V_{0}[/tex]) min = [tex]\sqrt{R g}[/tex]
     
    Last edited: Sep 13, 2008
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