Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 316 / 1 / ii

The impactors' number density per diameter is

K D_{im}^{- α} / V

π (D + D_{im})^{2} /4

R_{col} (D, D_{im}) d D_{im} = \frac{K D _{im}^{- α}}{V} \frac{π ( D + D _{im} ) ^{2}}{4} v_{rel} d D_{im} = A D_{im}^{2 - α} (1 + \frac{D}{D _{im}})^{2} d D_{im},

where

A = \frac{π K v _{rel}}{4 V} .

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