| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2013 |
| Session | November |
| Topic | Variable acceleration (1D) |
| Type | Related rates with point moving along a curve or two moving objects |
| Difficulty | Standard +0.8 This is a related rates problem requiring students to set up a distance function between two moving objects, differentiate to find when the rate of change is zero, then calculate the minimum distance. It involves coordinate geometry, Pythagoras, differentiation, and solving a quadratic—multiple non-trivial steps beyond standard kinematics exercises. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02a Kinematics language: position, displacement, velocity, acceleration |
7 At a given instant two stunt cars, $X$ and $Y$, are at distances 500 m and 800 m respectively from the point of intersection, $O$, of two straight roads crossing at right angles. The stunt cars are approaching $O$ at uniform speeds of $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $30 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively, one on each road. Find, in either order,\\
(i) the time taken to reach the point of closest approach,\\
(ii) the shortest distance between the stunt cars.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2013 Q7}}