# 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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