Up, Up, and Strictly Away

A ball with mass mm is thrown from the origin at speed V0V_{0} toward the right on an exotic planet where the strength of gravity is g=g10=1 m/s2.g^\prime = \frac{g}{10} = \SI[per-mode=symbol]{1}{\meter\per\second\squared}.

Let α\alpha be the largest possible angle such that, for all θ<α\theta<\alpha, the distance between the ball and its launch point will be strictly increasing for t>0t>0.

What is tan2α,\tan^{2} \alpha, to two decimal places?

Details and Assumptions:

  • V0=100 m/s.V_{0}=100 \text{ m/s}.
  • m=1 kg.m=1 \text{ kg}.

Bonus: Generalize this angle for arbitrary values of V0V_{0}, mm, and gg^\prime.


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