# physics

On a safari, a team of naturalists sets out toward a research station located 5.54 km away in a direction 47.9 ° north of east. After traveling in a straight line for 1.29 km, they stop and discover that they have been traveling 24.6 ° north of east, because their guide misread his compass. What are (a) the magnitude and (b) the direction (as a positive angle relative to due east) of the displacement vector now required to bring the team to the research station?

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1. D = 5.54km[47.9o] - 1.29km[24.60]

X = 5.54*cos47.9 - 1.29*cos24.6=2.54 km.
Y = 5.54*sin47.9 - 1.29*sin24.6=3.57 km.

Tan A = Y/X = 3.57/2.54 = 1.40691
A = 54.6o

Displacement = Y/sin A = 3.57/sin54.6 =
4.38km[54.6o].

a. Magnitude = 4.38 km.

b. Direction = 54.6o N of E.

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posted by Henry

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