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Reading through my homework, I encountered this. I don't know what a picture of this would look like, and how to decompose into separate vectors. Once I figure out what I need to decompose into, I can do the rest. Can you help me?

A car is driven east for a distance of 48 km, then north for 27 km, and then in a direction 32° east of north for 25 km. Determine (a) the magnitude (in km) of the car's total displacement from its starting point and (b) the angle (from east) of the car's total displacement measured from its starting direction.

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up vote 1 down vote accepted

Draw a picture. Piece by piece. Describing what it looks like just involves me repeating the problem. Draw a line segment right and label is 40. Draw a line segment up and label it 27, connected to the end of the previous line. Draw a line segment at an angle, label the degree 32 from upwards and the length 25. Then find the overall x and y displacement for the big triangle.

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HINT Take the unit vector along (positive) east to be $\mathbf i = (1,0)$, and that along north to be $\mathbf j = (0,1)$. Now, consider each of the three displacements, and decompose them into $\mathbf i$ and $\mathbf j$ components. The final position is just the vector sum of the displacements.

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