# Kinematics in 2D - Captain of a Plane Question

This is an assignment question, so I'm not looking for the answer but perhaps just a nudge in the right direction.

## Homework Statement

The captain of a plane wishes to proceed due west. The cruising speed of the plane is 260 m/s relative to the air. A weather report indicates that a 45.0-m/s wind is blowing from the south to the north. In what direction, measured with respect to due west, should the pilot head the plane?

## Homework Equations

This sounds like it's a right triangle, so I think Pythagorean theorem would be used.

c2 = a2 + b2

## The Attempt at a Solution

I was attempting to draw the problem on a standard x, y coordinate system but wasn't sure how to lay it out.

The wind seems pretty obvious as it's blowing from the south to north, so I was thinking about using a vector arrow pointing in the + y direction. The cruising speed of the plane however seems a little trickier. Would I consider this to be the hypotenuse? Or just one of the other two sides of the right triangle?

Once the two values have been drawn I imagine you would use Pythagorean to find the other side and then calculate the angle.

Any advice?

## Answers and Replies

Delphi51
Homework Helper
The 260 m/s vector begins at the end of the wind vector and goes at an angle so it ends up straight west of the starting point of the wind vector. The plane's speed with respect to the ground is the sum of the wind and 260 vector and you want it to be straight west.