I'm trying to solve a seemingly basic question but it seems to be taking me towards some advanced dynamics that is over my head. Any help would be appreciated. (If it matters, this is not a homework problem - I am simply curious about the answer and how to solve it.) 1. The problem statement, all variables and given/known data As the sun is setting (or rising), a tree casts a shadow on a flat field. Is it possible for a man to be jogging at the pace of the tree's advancing shadow at some point during sunset? If so, how tall should the tree be? Average speed of a running man: 6.71 meters/sec Angular Velocity of the Earth: .0042 degrees/sec 2. The attempt at a solution I've tried laying it out as a basic rate of change problem, but there are more factors at play here than I originally thought. An outline of my attempts: y=x/tan(θ) where dy/dt = 6.71m/s, dθ/dt = .0042 degrees/sec θ = the acute angle formed by top of the tree, the shadow being cast from it, and the tree itself. However, my math is faulty because this is not actually θ. θ is the rotation at the center of the earth, not the top of the tree. The sun sets at a different dθ/dt at the top of the tree than it does at the center of the earth. Therefore, I think it's more of a dynamics problem than a simple physics problem. I would appreciate some help finding the process by which to solve it.