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Problem No 1

A ballistic missile is launched from the north pole, the target is at the latitude \Phi (>0, if northern hemisphere, <0 otherwise). At which angle (with respect to the horizon)  the missile needs to be launched in order to have minimal launch velocity of the missile?


Remark: ballistic missile is like a stone: you give its initial velocity, and it moves due to inertia; you can neglect the air friction.


NB! When submitting your answer, please use the subject line "Problem No 1".

If you are not yet registered, you can still register and participate: just send the registration info (name, date of birth, etc.) together with  your answer.


Finally, what you may assume well-known and what not: things which are not in the formula sheet need to be motivated/derived. (You don't need to check – your typical high-school formulae are there.)

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