Cannon Ball r(t) - Find Max Ø for Increasing r2

[BreakingBad]

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.

 

[Mindscrape]

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