On a safari, a team of naturalists sets out toward a research station located 4.63 km away in a direction 38.7 ° north of east. After traveling in a straight line for 2.13 km, they stop and discover that they have been traveling 25.9 ° 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?

Question

Landen Cochran

Physics

30 March, 22:18

On a safari, a team of naturalists sets out toward a research station located 4.63 km away in a direction 38.7 ° north of east. After traveling in a straight line for 2.13 km, they stop and discover that they have been traveling 25.9 ° 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?

+2

Answers (1)

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Cesar Diaz · Answer 1

Exactly, it is a vector subtraction problem. Let t=theta,

t1=38.7, d1=4.63; t2=25.9, d2=2.13

v1=d1 =

v2=d2 =

Final vector

v3 = v1-v2

=

=

where

v3x=d1*cos (t1) - d2*cos (t2)

v3y=d1*sin (t1) - d2*sin (t2)

The final vector v3 has therefore a magnitude of

||v3||=sqrt (1.6973^2+1.9645^2) = 2.5962, and a direction of

theta=atan (1.9645/1.6973) = 49.17 degrees north of east

Note: all three vectors are in the direction of the first quadrant.