| Exam Board | OCR |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2004 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Interception: find bearing/direction to intercept (exact intercept) |
| Difficulty | Challenging +1.2 This is a standard M4 relative velocity/interception problem requiring conversion of bearings to vectors, setting up the interception condition (relative velocity parallel to relative position), and calculating relative velocity magnitude. While it involves multiple steps and vector manipulation, it follows a well-established method taught explicitly in M4 courses with no novel insight required. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02e Two-dimensional constant acceleration: with vectors |
3 From a speedboat, a ship is sighted on a bearing of $045 ^ { \circ }$. The ship has constant velocity $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in the direction with bearing $120 ^ { \circ }$. The speedboat travels in a straight line with constant speed $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and intercepts the ship.\\
(i) Find the bearing of the course of the speedboat.\\
(ii) Find the magnitude of the velocity of the ship relative to the speedboat.
\hfill \mbox{\textit{OCR M4 2004 Q3 [7]}}