# Frames of reference problem help(grade 12)

## Homework Statement

A boat goes at 7.78 m/s [37 degrees west of south] in a current of 2.41 m/s [5 degrees north of west]. Find the velocity compared to the bottom.

## Homework Equations

I think we use this: Vf2 = Vi2 + 2a x delta d

## The Attempt at a Solution

I drew a diagram but don't know how to post it here....

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Delphi51
Homework Helper
You must add the two vectors. They are in different directions, so it is a bit complicated. One method is to find the horizontal (East/west) and the vertical (north/south) components of each vector. Then add the horiz and vertical vectors separately. Sketch these two vectors head-to-tail to add them. You'll see that you need to find the hypotenuse to get the total and use some trig to find the direction.

An alternate method is to sketch the original vectors head-to-tail, then draw a line from beginning to end - the "resultant" or total of the other two vectors. This makes a triangle and you can solve for the resultant side using both the law of sines and the law of cosines.

Welcome to the Physics Forum!

AWESOME! I know how to do that. I did a lot of those where you add the x and y components to get the resultant displacement or velocity. And yes my diagram is a head-to-tail diagram. Ill do it that way. So the velocity I get will be the velocity compared to the bottom? I'll post my final answer can you check please?

And thanks for the fast reply I'll be visiting here quite often this is how I did it...is this right? Delphi51
Homework Helper
Take another look at your first diagram. It would be a good idea to show the x and y components on there. Both of the x components are in the same direction (left) so you get 2.4 + 4.68 = 7.08 to the left. You may wish to call this -7.08.
In the y direction, the 6.21 is down and the 0.21 up, so you get a total of 6.0 down.