Question

# On a safari, a team of naturalists sets out toward a research station located 4.8 km...

On a safari, a team of naturalists sets out toward a research station located 4.8 km away in a direction 42 degrees north of east. After traveling in a straight line for 2.4 km, they stop and discover that they have been traveling 22 degrees north of east, because their guide misread his compass. What are (a) the magnitude and (b) the direction (relative to due east) of the displacement vector now required to bring the team to the research station?

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First you need to convert all the vectors to cartesian coordinates.
The direction they were actually headed:
y = 2.4 * sin 22 = 0.899m
x = 2.4 * cos 22 = 2.225m

Where they need to end up:
y = 4.8* sin 42 = 3.212m
x = 4.8* cos 42 = 3.567m

Difference in x = 3.567m - 2.225m = 1.342m
Difference in y = 3.212m-0.899m = 2.313m

Converting to magnitude and angle
√2.3132 + 1.3422 = 2.674 m

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tan -1 (2.313/1.343) = 59.89o

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