PHYSICS! HELP PLEASE
posted by Allison on .
A shopper pushes a cart 43 m south down one aisle and then turns 90.0° west and moves 15 m. He then makes another 90.0° turn and moves 10 m.
(a) What is the largest possible displacement of the shopper?
______ m _____° counterclockwise from west
(b) What is the smallest possible displacement of the shopper?
______ m _____° counterclockwise from west

start the shopper at (0,0)
After pushing the cart 43 m south, he's now at (0, 43)
After turning west and pushing the cart 15 m, he's now at (15, 43)
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 (15, 53)
north will result in the smallest displacement from the origin . . . then he'd be at (15, 33)
The distance from the origin for the largest displacement is (15^2 + 53^2)^0.5
Let the angle counterclockwise from west be x: then
tan x = 53/15
The distance from the origin for the smallest displacement is (15^2 + 33^2)^0.5
at an angle:
tan x = 33/15