Posted by Bob on Tuesday, September 4, 2012 at 11:42pm.
start the shopper at (0,0)
After pushing the cart 50 m south, he's now at (0, -50)
After turning west and pushing the cart 19 m, he's now at (-19, -50)
Now he has to turn 90 degrees again. . . he will then be going either north or south. . . south will result in the largest displacement from the origin. . . now he's at (-19, -63)
north will result in the smallest displacement from the origin . . . then he'd be at (-19, -37)
The distance from the origin for the largest displacement is (19^2 + 63^2)^0.5
Let the angle counterclockwise from west be x: then
tan x = 63/19
The distance from the origin for the smallest displacement is (19^2 + 37^2)^0.5
at an angle:
tan x = 37/19
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