As she picks up her riders, a bus driver traverses four successive displacements
ID: 1406928 • Letter: A
Question
As she picks up her riders, a bus driver traverses four successive displacements represented by the expression
(-6.1 b) - (3.70 b cos 40°) - (3.70 b sin 40°) + (3.40 b cos 50°) - (3.40 b sin 50°) - (5.10 b)
Here b represents one city block, a convenient unit of distance of uniform size; is east; and is north. The displacements at 40° and 50° represent travel on roadways in the city that are at these angles to the main east—west and north—south streets.—256, March 1999.">†
(c) Compute the magnitude and direction of her total displacement.
magnitude
b
direction
° counterclockwise from east
magnitude
b
direction
° counterclockwise from east
Explanation / Answer
Total distance is 6.1+3.7+3.4+5.1= 18.3 blocks
(-6.1) - (3.70cos 40°) + (3.40cos 50°) = -6.749 (or 6.749 b locks west)
Add up your y (north) distances:
-(3.70 sin 40°) - (3.40 sin 50°) - (5.10) = -10.08 b North (or 10.08 blocks south)
Magnitude is 12.13 b
tan^-1(-10.08/-6.749)= 56.2 but since it is in third quadrant, add 180 degrees to get a final angle of 236.2 degrees.
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