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 \(v_0\). Due to wind, it gathers some horizontal velocity \(v_x = ay\), where \(a\) is a constant and \(y\) is the height from the surface of the Earth.

The normal acceleration of the balloon as a function of \(y\) is

Image credit: Wikipedia Tiia Monto
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