Rolling Ball

A uniform solid ball of mass $$m$$ rolls without slipping down a wedge of mass $$2m$$ and angle $$45^\circ$$, which itself can slide without friction on a horizontal floor. The acceleration of the ball relative to the wedge can be expressed as $$\dfrac{p}{q}\sqrt{2}g$$, where $$g$$ denotes the gravitational acceleration. Calculate $$q-p$$.

×