Terminal velocity of an object on an inclined plane?

An object is on an inclined plane of angle \(\theta\) with the horizontal. It is given an initial velocity of \(V_0\) in the sideways direction (i.e. perpendicular to the down-hill direction). If the coefficient of friction is \(\mu=\tan\theta\), then find the terminal velocity of the object. (Neglect air resistance.)

If the terminal velocity can be expressed as \(V_{\text{terminal}}=kV_0\) and \(k\geqslant 0\), then find \(k\).

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