(adsbygoogle = window.adsbygoogle || []).push({}); 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 r^{2}as x^{2}+ y^{2}, and then find the condition that r^{2}is always increasing.]

2. Relevant equations

r(t) = gt^{2}/2 + v_{0}t + x_{0}

r^{2}= x^{2}+ y^{2}

x = rcosØ

y = rsinØ

3. The attempt at a solution

r^{2}= (gt^{2}/2 + v_{0}t + x_{0})(gt^{2}/2 + v_{0}t + x_{0}) = x^{2}_{0}+ 2x_{0}v_{0}t + x_{0}gt^{2}+ v^{2}_{0}t^{2}+ v_{0}gt^{3}+ g^{2}t^{4}/4 = x^{2}+ y^{2}= r^{2}(cos^{2}Ø + sin^{2}Ø)

I don't know how to solve for Ø, so that r^{2}is always increasing.

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# Homework Help: Cannon Ball r(t)

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