Hint. Apply conservation of mechanical energy to the system consisting of the two blocks, the pulley, the string, and the earth. The mechanical energy at the initial instant when the blocks start moving is equal to the final mechanical energy when block 2 has elevation h_f. The final mechanical energy involves the final speed v_f via the kinetic energies of the two blocks at that instant. Thus, energy conservation yields an equation for v_f that can be solved.