| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2017 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Projectile with plane collision |
| Difficulty | Standard +0.8 This M4 question requires understanding of oblique impacts on inclined planes, resolving velocities into components parallel and perpendicular to the plane, and applying Newton's experimental law. While the vector notation and inclined plane geometry add complexity beyond basic collision problems, the solution follows a systematic method taught in M4. It's harder than average A-level but standard for Further Maths mechanics. |
| Spec | 6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
4. [In this question, the unit vectors $\mathbf { i }$ and $\mathbf { j }$ are in a vertical plane, $\mathbf { i }$ being horizontal and $\mathbf { j }$ being vertically upwards.]
A line of greatest slope of a fixed smooth plane is parallel to the vector $( - 4 \mathbf { i } - 3 \mathbf { j } )$. A particle $P$ falls vertically and strikes the plane. Immediately before the impact, $P$ has velocity $- 7 \mathbf { j } \mathrm {~ms} ^ { - 1 }$. Immediately after the impact, $P$ has velocity $( - a \mathbf { i } + \mathbf { j } ) \mathrm { ms } ^ { - 1 }$, where $a$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Show that $a = 6$
\item Find the coefficient of restitution between $P$ and the plane.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2017 Q4 [8]}}