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Projectile angle help

  1. Dec 11, 2007 #1
    1. The problem statement, all variables and given/known data

    [​IMG]

    So, we have a body that is launched at a certain angle with initial velocity of 20m/s.
    The body is supposed to hit an object, which is 20m further away (horizontally), at the height of 5m. The question is at what angle should the body be launched.

    2. Relevant equations
    The equation for the horizontal coordinate is which is 20 is X=v*cos(alpha)*t ,
    while the one for the vertical coordinate which is 5 is Y=v*sin(alpha)*t - (1\2)*g*t^2.


    3. The attempt at a solution

    I expressed time(t) from the first equation and got t=X/v*cos(alpha), substituted it in the second equation, and received Y=v*sin(alpha)*X/v*cos(alpha) -5 * (x/v*cos(alpha))^2, with Y being 5 and X 20.

    However after simplifying the equation i received 4*tan(alpha) - sec^2(alpha) - 1 = 0, from where i could not express the angle alpha, therefore i could find its value.

    If you have any suggestion of how to solve the problem please assist me.
     
    Last edited: Dec 11, 2007
  2. jcsd
  3. Dec 11, 2007 #2

    Doc Al

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    Staff: Mentor

    Hint: Use a trig identity to rewrite [itex]\sec^2\alpha[/itex] in terms of [itex]\tan^2\alpha[/itex].
     
  4. Dec 11, 2007 #3
    Of course....how could I have missed that...thanks a lot, i solved it :).
     
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