2. Two small smooth spheres \(A\) and \(B\) have equal radii. The mass of \(A\) is \(2 m \mathrm {~kg}\) and the mass of \(B\) is \(m \mathrm {~kg}\). The spheres are moving on a smooth horizontal plane and they collide. Immediately before the collision the velocity of \(A\) is \(( 2 \mathbf { i } - 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and the velocity of \(B\) is \(( - 3 \mathbf { i } - \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Immediately after the collision the velocity of \(A\) is \(( \mathbf { i } - 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find the speed of \(B\) immediately after the collision.
(5)

## Question 2:

| Working/Answer | Marks | Notes |
|---|---|---|
| $2m(2\mathbf{i}-2\mathbf{j})+m(-3\mathbf{i}-\mathbf{j}) = 2m(\mathbf{i}-3\mathbf{j})+m\mathbf{v}$ | M1 A1 | |
| $(\mathbf{i}-5\mathbf{j}) = (2\mathbf{i}-6\mathbf{j})+\mathbf{v}$ | A1 | |
| $(-\mathbf{i}+\mathbf{j}) = \mathbf{v}$ | | |
| $|\mathbf{v}| = \sqrt{(-1)^2+1^2} = \sqrt{2}$ m s$^{-1}$ | DM1 A1 | cwo, **Total: 5** |

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2. Two small smooth spheres $A$ and $B$ have equal radii. The mass of $A$ is $2 m \mathrm {~kg}$ and the mass of $B$ is $m \mathrm {~kg}$. The spheres are moving on a smooth horizontal plane and they collide. Immediately before the collision the velocity of $A$ is $( 2 \mathbf { i } - 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ and the velocity of $B$ is $( - 3 \mathbf { i } - \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$. Immediately after the collision the velocity of $A$ is $( \mathbf { i } - 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$.

Find the speed of $B$ immediately after the collision.\\
(5)\\

\hfill \mbox{\textit{Edexcel M4 2008 Q2 [5]}}