Mathematics 9709 · AS & A Level · Momentum

Momentum — practice question

Particles $P$ and $Q$, with masses $m\text{ kg}$ and $2\text{ kg}$ respectively, are free to move on a smooth horizontal plane. They travel directly towards one another at speeds $u\text{ m s}^{-1}$ and $3u\text{ m s}^{-1}$ respectively. A collision takes place, and the direction of motion of each particle is reversed by the impact. Immediately after the collision, the speed of $P$ is $\frac{u}{3}\text{ m s}^{-1}$.
(a)[3]

Find, in terms of $m$ and $u$, an expression for the velocity of $Q$ after the collision, and hence show that $m > 4.5$.

(b)[4]

Since $m$ is an integer, determine the greatest possible value of $m$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Momentum conservation gives: $mu+2(-3u)=m\left(-\frac13u\right)+2v$

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