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Pseudo Orbital motion only due to Coriolis force

Planet, say of mass M and radius R is rotating with some angular velocity ω and a object of mass m (initially on the surface and rotating with the planet) was launched with velocity v vertically ...
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With what vel. would you have to launch an object vertically up from the earth's surface for it to land back again at it's initial launching point?

[Can skip reading this part] First of all, Newtonian gravity shall be considered whilst trying to solve this question. It's been on my mind for a long, long time and has been bothering me since. I ...
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