A student has stolen the MAT100 final exam from the vault in Alice?s home. Luckily, we had placed a microchip on the exam. There are two radar sources that track the microchip, one at Alice?s home and one at the math department. Alice?s home is exactly 14 km North of the math department. At a given time, the radar in Alice?s home indicates that the distance from the thief to Alice?s home is 15 km, and it is increasing at a rate of 31.2 km/h. At the same time, the second radar indicates that the distance from the thief to the math department is 13 km and it is decreasing at a rate of 20 km/h. How fast is the thief moving at that given time, and in which direction?
Hint: If you do not know how to start, it may be helpful to choose a set of axes and give names to the coordinates of the thief on that axis.
Warning: Beware of solving this problem ?without calculus?. If you use results from vector geometry, linear algebra, and physics (such as relating velocity and rate of change of distances using projections) you are assuming a lot of results, and you have to prove any result that is not part of this course. Proving those results takes the same effort as solving this problem directly with calculus.
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