How Do You Calculate the Missing Vector in a Sailor's Journey?

[me!ü]

Homework Statement

A sailor in a small sailboat encounters shifting winds. She sails 2.00 km east, then 3.50 km southwest, and then an additional distance in an unknown direction. Her final position is 5.80 km directly east of the starting point. Find the magnitude and direction of the third leg of her journey.

Homework Equations

The Attempt at a Solution

 

[Patta1667]

Have you done any work on the problem? Try drawing it out and labeling the distances, do you know how to find the length of the sides of an isosceles (two sides same length) triangle?

 

[me!ü]

No, I haven't done anything yet. I don't know what to do. Nor solve for those sides.

 

[Pinu7]

Try to turn these vectors from polar coordinates to Cartesian coordinates(normal vectors).

For example, (2 km,east)=(2 km,0^o). Changing that into Cartesian gives <2cos 0^o km,2 cos 0^o km> =<2(1) km,2(0)km>=<2km,0km>

Then do that for all of them and add their components.

You may want to see this: http://www.delphiforfun.org/programs/math_topics/polar-cartesian.htmEDIT: Also, http://www.1728.com/vectutor.htm

 

[me!ü]

Try to turn these vectors from polar coordinates to Cartesian coordinates(normal vectors).

For example, (2 km,east)=(2 km,0^o). Changing that into Cartesian gives <2cos 0^o km,2 cos 0^o km> =<2(1) km,2(0)km>=<2km,0km>

Then do that for all of them and add their components.

You may want to see this: http://www.delphiforfun.org/programs/math_topics/polar-cartesian.htm


EDIT: Also, http://www.1728.com/vectutor.htm

Can I get the magnitude and direction of the missing vector with that?