A machine for driving a nail into a block of wood causes a hammerhead to drop vertically onto the top of a nail. The mass of the hammerhead is 1.2 kg and the mass of the nail is 0.004 kg (see diagram). The hammerhead hits the nail with speed \(v \text{ m s}^{-1}\) and remains in contact with the nail after the impact. The combined hammerhead and nail move immediately after the impact with speed 40 \(\text{ m s}^{-1}\).

(a) Calculate \(v\), giving your answer as an exact fraction.

(b) The nail is driven 4 cm into the wood. Find the constant force resisting the motion.