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Help with level 5 Isaac Physics question

A ball is thrown at speed v from the origin. What is the minimum angle to the vertical at which the ball can be thrown so that its distance to the origin is always increasing. Ignore Air Resistance.

So for this question I first found an equation for the the distance from the origin at an given time in terms on v, t and θ (the angle to the vertical) as:

d = sqrt (x2 + y2)
= sqrt (v2t2sin2(θ) + (vtcos(θ) - 1/2gt2sin(θ))2)

I then setup an inequality such that the rate of change in d2 with respect to time is > 0 instead of the rate of change in d with respect to time to get rid of the square root and make things easier. I am not sure what to do after this. There must be a way of removing the v since it is not given in the question and does not affect the minimum angle. Please help, thanks.

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