Block 1 of mass \displaystyle 3m is sliding along a frictionless horizontal table to the right with speed \displaystyle v_0. Block 1 collides with block 2 of mass \displaystyle m that is moving to the left with speed \displaystyle v_0. After the collision, the two blocks stick together and the blocks enter a rough surface at \displaystyle x=0 with a coefficient of kinetic friction that increases with distance as \displaystyle \mu (x)=b x^2 for \displaystyle 0\leq x\leq d, where \displaystyle b is a positive constant. The blocks come to rest at \displaystyle x=d. The downward gravitational acceleration has magnitude \displaystyle g. Determine an expression for the initial speed \displaystyle v_0 of the blocks.
