# Projectile motion question (about angles)?

If I launch a projectile, what is the maximum angle at which I can launch the object such that the distance between the object and the launching device never decreases?
My thought is that i should look at the position, say r=sqrt(x^2+y^2) -- where x = v0cos(theta)t and y=v0sin(theta)t-(1/2)gt^2 and take time...
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If I launch a projectile, what is the maximum angle at which I can launch the object such that the distance between the object and the launching device never decreases?

My thought is that i should look at the position, say r=sqrt(x^2+y^2) -- where x = v0cos(theta)t and y=v0sin(theta)t-(1/2)gt^2 and take time derivative, to get the velocity and set the velocity equal to zero. Then we could potentially solve for theta. (Another thought I had but I'm not sure it would tell me much, is to take the derivative of r w.r.t. theta instead of time and set equal to zero etc...) Either way, I've got a t left in the equation for theta. Is this method right, is there a way to get rid of the time dependence? Thanks!

My thought is that i should look at the position, say r=sqrt(x^2+y^2) -- where x = v0cos(theta)t and y=v0sin(theta)t-(1/2)gt^2 and take time derivative, to get the velocity and set the velocity equal to zero. Then we could potentially solve for theta. (Another thought I had but I'm not sure it would tell me much, is to take the derivative of r w.r.t. theta instead of time and set equal to zero etc...) Either way, I've got a t left in the equation for theta. Is this method right, is there a way to get rid of the time dependence? Thanks!

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