| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2013 |
| Session | November |
| Topic | Impulse and momentum (advanced) |
| Type | Collision with fixed wall |
| Difficulty | Challenging +1.2 This is a structured multi-part mechanics question requiring resolution of velocities parallel and perpendicular to a wall, application of Newton's law of restitution, and impulse calculation. Part (i) is a guided 'show that' using dot product or angle formulae. Parts (ii)(a) and (ii)(b) follow standard procedures once components are resolved. While it requires careful vector decomposition and multiple steps, the techniques are all standard A-level Further Maths mechanics with clear scaffolding, making it moderately above average difficulty but not requiring novel insight. |
| Spec | 6.03c Momentum in 2D: vector form6.03d Conservation in 2D: vector momentum6.03f Impulse-momentum: relation6.03g Impulse in 2D: vector form6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
11 A smooth sphere of mass 2 kg has velocity $( 24 \mathbf { i } - 7 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ and is travelling on a horizontal plane, where $\mathbf { i }$ and $\mathbf { j }$ are perpendicular unit vectors in the horizontal plane. The sphere strikes a vertical wall. The line of intersection of the wall and the plane is in the direction $( 4 \mathbf { i } + 3 \mathbf { j } )$.\\
(i) Show that the acute angle between the path of the sphere before the impact and the direction of the wall is $\tan ^ { - 1 } \left( \frac { 4 } { 3 } \right)$.\\
(ii) After the impact, the velocity of the sphere is $( 7.2 \mathbf { i } + 15.4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$. Find
\begin{enumerate}[label=(\alph*)]
\item the coefficient of restitution between the sphere and the wall,
\item the magnitude of the impulse exerted by the sphere on the wall.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2013 Q11}}