Fireworks
Author: Danby, J.M.A.
College Mathematics Journal, Vol. 23, no. 3, pp. 237-240, 1992.
In this article, Danby models the motion of fireworks. Differential equation can be used to model the motion of fireworks close to the earth's surface (thus experiencing the pull of gravity). The motion begins at the same initial position but with different initial velocities. Danby begins by constructing a model for fireworks which only experience the force of gravity. In this case, the motion of the firework will lie on a sphere. Since this is unrealistic of fireworks in the real world, he goes on to add in a resistance term which acts on the fireworks. Resistance is more realistically modeled by a force which is proportional to the k-th power of the particle's speed. For any power law of resistance, particles lie on expanding circles. (Summary by Anna Cho, Pomona College '13)