1. The problem statement, all variables and given/known data A pilot attempts to y with constant speed v from the point P = (D; 0) on the x-axis to the origin O = (0; 0). A wind blows with speed w in the positive y direction. The pilot is not familiar with vector addition and thinks the shortest path to O is achieved by ying his plane so that it always points directly towards O. (a) Show that the actual flight path of the plane (in Cartesian coordinates) is given by y(x) = f(x) sinh[g(x)]; where f(x) and g(x) are scalar functions of x that are to be determined. 2. Relevant equations No formula's given but we have been working with tangential and normal accelation components 3. The attempt at a solution The plane always points towards to origin. So I would assume the force of the engines is directed towards the origin. This I would assume the solution to be a(t) = -m(t)*x(t) or a(x) = -n(x) * (x,y(x)) I am not sure how to handle the wind. It would seem out of place to do something with draf forces given the content of the course but I am not really that into physics so who knows. It may just be an initial velocity. Or that everything the pilot does is relative to the moving air. I also though of this expression for the velocity v(t) = -v*x(t)/|x(t)| +w*jhat That I can actually treat as a system of linear equations but the solution seems complicated too complicated for this course. My thought is that once I get the right differential equation I just show that the proposed form in the question satisfies that differential equation. Please Help. Thanks in advance.