Over the years, I've seen several questions in mathematics that can be solved using concepts borrowed from Physics. Having seen these question, I'm interested to find out what other mathematics questions you've found that can be better solved with a concept from physics - or at least where the application of physics is interesting and perhaps illuminating.
Examples
One of these questions is on minimizing the time taken for a lifeguard to go out to a stationary distressed swimmer. In the scenario, the lifeguard runs faster than he swims in the water, and as such the straight line is not the fastest way for the lifeguard to reach the swimmer. Students will normally use calculus to solve this problem, and the answer can be obtained after some work - however, a much more convenient (and intuitive) way is to borrow from the idea of refractive indices in geometric optics. We recast the situation by replacing the beach and the sea with two materials with different refractive indices, choosing the appropriate refractive indices proportionate to the ratio between the lifeguard's velocities while running and swimming. The problem is then reduced to finding a beam of light that passes through both the swimmer and the lifeguard's position. (For a more complete explanation, you can visit this site: http://findingmoonshine.blogspot.sg/2012_05_01_archive.html)
Another of these questions requires one to prove that, in an acute-angled triangle, the angle subtended by any side of the triangle at the Toricelli point is 120°. Again, instead of using trigonometry, one can use the concept of hanging equal weights from a (frictionless) string at each of the vertices of the triangle, and then tying each of the three strings together at one knot placed on the surface of the triangle. The equilibrium position of the knot is the Toricelli point, and one can then complete the proof by considering forces acting on the knot.
Looking forward to hearing from you!
