A ramp of mass M and angle with respect to the horizontal x-axis rests on a horizontal frictionless plane. On the inclined plane of the ramp rests a small block of mass m, initially a distance h above the horizontal plane. The surface of the ramp is also frictionless. Both the mass and the ramp can move (and will start to do so in opposite directions). Assume the horizontal motion is in the x-direction and the vertical coordinate is z. Use the Lagrangian formalism to determine the equations of motion for the ramp and the block. Then use the method of Lagrange-multipliers to determine the normal force of the ramp on the block.