Frames of reference problem help(grade 12)

AI Thread Summary
To find the velocity of a boat in a current, the vectors of the boat's speed and the current must be added together. This involves breaking down each vector into horizontal and vertical components and then combining these components separately. A head-to-tail diagram can be used to visualize the addition of vectors, forming a triangle to determine the resultant velocity. The calculations show that the total horizontal component is -7.08 m/s (to the left) and the vertical component is -6.0 m/s (down). The final velocity compared to the bottom can then be derived from these components.
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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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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.

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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 :biggrin: I'll be visiting here quite often :biggrin:
 
this is how I did it...is this right?

17tjbs.jpg
 
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.
 
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