3 - The Case of the Swiveling Spotlight—Solution

Summary

Your Honor,

The defense proposes to show that if the defendant were traveling at the speed that the police witnesses claimed to have measured, then he could not have been under observation for as long as the 20-second minimum that the law requires. We will establish this by deriving an equation whose root T is the time (in seconds) that would have elapsed from when the defendant's car was first observed until the time when the spotlight on the police cruiser would have been pointing directly sideways. According to the testimony from Sergeants Preston and Renfrew, T is larger than the time that the defendant's car was actually under observation.

We will derive a series of approximations to T. We will show that each of these approximations is larger than T, and that one of them is less than 20. From this we will conclude that T is less than 20, and hence that the defendant's car was under observation for less than the 20 seconds required by law.

Consider a system of coordinates imposed on a map of Park du Portage and its surroundings (see Exhibit A). The X-axis is tangent to the parabolic boulevard at its vertex, and the Y-axis is the north-south line passing through the vertex of the boulevard. Hence the origin is at the vertex. The south boundary road, along which the defendant's car traveled, now forms a horizontal line below the X-axis. The fountain in Park du Portage is at the focus of the boulevard, directly north of the vertex as shown on the map, on the positive Y-axis.