Physics or math?
Find the maximum angle with the horizontal with which a projectile may be projected on earth so that its distance from the point of projection continuously increases.
Give your answer in degrees and up to 2 decimal places.
Assume we neglect variation of gravity.
The answer is 70.52.
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Let the position vector magnitude be r.then, r^2=x^2+y^2.differentiating the equation we get:(this will give expression for max distance) X/Y=-Vx/Vy solving this we will get a quadratic in t(time). for the distance to be increasing there should be no max distance or no real value of time. so in the quadritic equation(in t),putting b^2<4ac , we get sin(theta)<sqrt(8/9) theta<sin^-1(sqrt(8/9))~70.52.