A proton $($mass $1$ u$)$ is shot toward an unknown target nucleus at a speed of $2\mathrm{.}5010^6$ m$/$s$.$ The proton rebounds with its speed reduced by $25\%$while the target nucleus acquires a speed of $3\mathrm{.}6510^5$ m$/$s$.$ What is the mass, in atomic mass units, of the target nucleus?

Express your answer in atomic mass units.