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Trajectory of a ball

  1. Sep 24, 2013 #1
    1. The problem statement, all variables and given/known data

    A cannon shoots a ball at an angle [itex]\theta[/itex] above the horizontal ground

    a) Neglecting air resistence, find the ball's position (x(t) and y(t)) as a function of time.

    b) Take the above answer and find an equation for the ball's trajectory y(x).


    2. Relevant equations

    [itex]\frac{dx}{dt}[/itex] = Vocos([itex]\theta[/itex])

    [itex]\frac{dy}{dt}[/itex] = Vosin([itex]\theta[/itex]) - gt


    3. The attempt at a solution

    Okay, so I integrated both sides of both equations and ended up with:

    x(t) = Vocos([itex]\theta[/itex])t

    y(t) = Vosin([itex]\theta[/itex])t - 0.5gt2

    which I'm pretty sure solves part a), but I'm having a lot of trouble finding a function of y in terms of x for part b). I tried messing around with some trigonometric identities but I get nowhere. Any tips?
     
    Last edited: Sep 24, 2013
  2. jcsd
  3. Sep 24, 2013 #2
    Try to find t in terms of x or y from one of the equations you found for part a. Substitute that in the other equation.
     
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