Rising Balloon!

A balloon starts rising from the surface of earth. The vertical component of the balloon's velocity is constant and it's equal to v0v_0. Due to wind, it gathers some horizontal velocity vx=ayv_x = ay, where aa is a constant and yy is the height from the surface of the Earth.

The normal acceleration of the balloon as a function of yy is

Image credit: Wikipedia Tiia Monto
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