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Homework Help: Kinematics Trig Problem

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data
    A football kicker can give the ball an initial speed of 25 m/s. What are the least and greatest elevation angles at which he can kick the ball to score a field goal from a point 50 m in front of goalposts whose horizontal bar is 3.44 m above the ground?

    3. The attempt at a solution
    I've worked it down to 3.44(cos a)^2 = 50(sin a)(cos a) - 19.6 , but I can't figure out how to solve this equation. None of the trig identities seem to help. Is this equation solvable (without a graphing calculator) or am I just approaching the problem the wrong way?
    Last edited: May 2, 2010
  2. jcsd
  3. May 2, 2010 #2
    2sin(a)cos(a) = sin(2a)
    cos(2a) = 2cos(a)^2 - 1
  4. May 2, 2010 #3
    Made the subs, now I have 1.72 cos(2a) - 25 sin(2a) = -21.32 . What now?
    Last edited: May 2, 2010
  5. May 2, 2010 #4


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    Homework Helper

    Assuming you did everything correctly, you can use the identity cos(2a)=1-2sin^2(a) to get a quadratic equation.
  6. May 2, 2010 #5
    Wouldn't I have to either get everything in terms of (sin a) or everything in terms of (sin 2a) to solve as a quadratic?
  7. May 3, 2010 #6
    You can subsitute cos(2a) = (1-sin^2(2a))^0.5 and square the equation to get a quadratic equation. Solve for sin(2a).
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