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    (Original post by TeeEm)
    Lagrangian considerations make it at least M9 ....
    Apropos de not-very-much, we can see that the particle remains on the cone if

    R \ge 0 \Rightarrow g\tan\alpha \ge \frac{a^2U^2}{r^3} \Rightarrow r \ge (\frac{a^2U^2}{g \tan\alpha})^{1/3}

    Now since r increases with time, and the all the other quantities involved in the condition are constants, then as long as that condition holds initially, then the particle will always remain on the cone i.e. if you want it to leave the cone, you have to do it by making its initial velocity too large for its initial height.
 
 
 
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Updated: March 9, 2016

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