A small fish $($m $=0\mathrm{.}5$ kg$)$ running away from the bigger fish at $0\mathrm{.}5$ m$/$s is swallowed by a bigger fish $($m $=4\mathrm{.}5$ kg$)$ chasing it at $3\mathrm{.}5$ m$/$s $($both move in the same direction$).$

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a$)$ What is the total momentum of this system before the big fish had its lunch?

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b$)$ What is the momentum after lunch?

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c$)$ how fast does the big fish move immediately after lunch $($perfectly inelastic collision$)?$

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d$)$ Calculate the total initial kinetic energy and total final kinetic energy. Is the kinetic energy conserved?