2
\includegraphics[max width=\textwidth, alt={}, center]{99f20949-471d-4da3-a680-ec24abf6baa5-03_510_604_260_769} 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 \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and remains in contact with the nail after the impact. The combined hammerhead and nail move immediately after the impact with speed \(40 \mathrm {~ms} ^ { - 1 }\).

1. Calculate \(v\), giving your answer as an exact fraction.
2. The nail is driven 4 cm into the wood. Find the constant force resisting the motion.