Openstax College Physics Map Openstax presented by Sapling Learning The colored

Question

Openstax College Physics Map Openstax presented by Sapling Learning The colored lines in the figure below represent paths taken by different people walking around in a city. Assume that each city block is 110 m long W- E Number What is the total distance traveled by the person walking along path A? Find the magnitude and direction of the displacement of path A. Click on the map to draw arrows directly on the figure. See the hint in the lower panel for tips on using the vector drawing tool. Number Number (counter-clockwise up from due east)

Explanation / Answer

First start with defining vector A:
This is at an angle of 42.9° to x-axis, so it can be written as
A = p cos(42.9) i + p sin(42.9) j
p being the magnitude of A
Similarly for B,
B = q cos(28.2) i + q sin (28.2)j
C is given as 25.8 j
also we have,
A+B+C = 0;
so [p cos(42.9) + q cos(28.2)] i + [p sin(42.9) + q sin(28.2)+ 25.8] j =0
i.e.
p cos(42.9) + q cos(28.2) = 0 ---> p/q = cos(28.2) / cos(42.9) = 1.203 ................. (1)
and
p sin(42.9) + q sin(28.2)+ 25.8= 0 ---> p sin(42.9) + q sin(28.2) + 25.8 = 0
but from equation (1),
p = 1.203 x q
so,
1.203 x q x sin(42.9) + q x sin(28.2) + 25.8 = 0
--> q =25.8 /(sin(42.9) x 1.203 + sin(28.2))
= 25.8 /1.29 = 19.98

so magnitude of A = p = 1.203 x 19.98 = 24.036 m
and magnitude of B = q = 19.98 m

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