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BreakingBad
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Homework Statement
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.]
Homework Equations
r(t) = gt2/2 + v0t + x0
r2 = x2 + y2
x = rcosØ
y = rsinØ
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.