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 1.2kg and the mass of the nail is 0.004kg (see diagram).
The hammerhead hits the nail with speed vms⁻¹ and remains in contact with the nail after the impact.
The combined hammerhead and nail move immediately after the impact with speed 40ms⁻¹.

Q: What topic does this question test?

This question tests Mechanics in A-Level Mathematics (syllabus code 9709). It is worth 5 marks.

Q: Which exam paper is this question from?

This question appeared in the Cambridge A-Level Mathematics Oct/Nov 2023 examination, Paper 4 Variant 3 (9709_w23_qp_43.pdf).

Question

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 1.2kg and the mass of the nail is 0.004kg (see diagram).
The hammerhead hits the nail with speed vms⁻¹ and remains in contact with the nail after the impact.
The combined hammerhead and nail move immediately after the impact with speed 40ms⁻¹.

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