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

When

u_{1} = V /3

, the downstream speed in the shock frame is

2 V /3

. Mass conservation gives

ρ_{0} V = ρ_{1} \frac{2 V}{3},

so

\frac{ρ _{1}}{ρ _{0}} = \frac{3}{2} .

Solved by gpt-5.6-sol high.

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