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Homework Help: Cannon Ball r(t)

  1. Sep 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Question: A cannon shoots a ball at angle Ø above the horizontal ground. Neglecting air resistance, and letting r(t) denote the ball's distance from the cannon, What is the largest possible value of Ø if r(t) is to increase throughout the ball's flight? [hint: Write down r2 as x2 + y2, and then find the condition that r2 is always increasing.]

    2. Relevant equations

    r(t) = gt2/2 + v0t + x0
    r2 = x2 + y2
    x = rcosØ
    y = rsinØ

    3. The attempt at a solution

    r2 = (gt2/2 + v0t + x0)(gt2/2 + v0t + x0) = x20 + 2x0v0t + x0gt2 + v20t2 + v0gt3 + g2t4/4 = x2 + y2 = r2(cos2Ø + sin2Ø)

    I don't know how to solve for Ø, so that r2 is always increasing.
  2. jcsd
  3. Sep 14, 2010 #2
    1) There shouldn't be any gravity in the x-direction.
    2) You have to find dr^2/dt > 0 if r^2 is going to always increase
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