- #1

Altheides

- 2

- 0

## Homework Statement

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.

## Homework Equations

No formula's given but we have been working with tangential and normal acceleration components

## 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.