2. Leigh and David are playing a game of laser tag!. David has managed to climb aboard a mining cart travelling along a parabolic track, while Leigh has been caught exposed trying to walk along a narrow path on the edge of a cliff. As long as David is in the cart he can only fire his laser at right angles to the direction of motion. If Leigh is caught in David's sight line he is doomed, but he can see a gap between the cliff and some rocks ahead of him. If he can get far enough into the gap David will not be able to see him and tag him. A rough schematic of the situation is sketched below. Cart Tracks David Direction of Fire Rocks Leigh Safety Cliff Edge This situation can be modelled on the cartesian plane as follows, where all quantities are measured in SI units: • Let s e [0, 0) be a variable representing time. • Leigh's position is represented by a point that travels along the r-axis, starting at the origin, with a positive constant speed v. • David's position is represented by a point that travels along the parabola y = (2x – 3)2 +5 so that at time s the r-coordinate is s.

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