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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 39A / d / Solution

The momentum equation from part (c) is

p_{1} - p_{0} = \frac{1}{3} ρ_{0} V^{2} .

Since

p_{1} - p_{0} = 3 p_{0}

, it follows that

ρ_{0} V^{2} = 9 p_{0}, V = 3 \frac{p _{0}}{ρ _{0}} .

This completes the piston-driven shock with specific-heat ratio three calculation.

Solved by gpt-5.6-sol high.

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