Boat Positioning: Lorraine and Jeff's Displacement in Race - Homework Question

[Rasofia]

Homework Statement

Lorraine steered her boat out of the harbor, heading east. She traveled 500 m to one buoy and then turned north and headed 300 m to another buoy. Jeff also left the harbor from the same point, and traveled 300 m [N] to a buoy, and then went 500 m [E].
a) What is the position of Jeff's boat relative to Lorraine's boat after they finish moving?
b) If Lorraine and Jeff race straight back, in what direction are they headed?[/B]

Homework Equations

The Attempt at a Solution

Okay, for letter a, I was a bit confused because are they not in the same position? They end up in the same place. But I guess technically Jeff's position would be west relative to Lorraine's boat?
For letter b, I said southwest, because they first go north east. Correct or not?

Thanks for your help :)[/B]

 

[Bystander]

technically Jeff's position would be west relative to Lorraine's boat?

Unless he rammed her and one or both boats sank.
SW is good. There is a possibility that they want a compass heading in degrees. Remember enough trig to calculate that?

 

[Rasofia]

Unless he rammed her and one or both boats sank.
SW is good. There is a possibility that they want a compass heading in degrees. Remember enough trig to calculate that?

I used tangent inverse (y/x) and got around 31 degrees so maybe that's it?
I don't really know if that would be the right equation for this though.

 

[Bystander]

be the right equation for this though.

That's perfectly good. Compass headings for mariners start with 0 degrees at due north, proceed clockwise through 90 (E), 180 (S), 270 (W), and back to 360 (a full circle) reset to 0 (N). So you've got 270 - 31 rather than 225 which would be a nitpicker's SW. Hand them the number and SW or WSW and you are in business.