A shopper pushes a cart 41 m south down one aisle and then turns 90.0° west and moves 28 m. He then makes another 90.0° turn and moves 14 m.

Question

(a) What is the largest possible displacement of the shopper?


____m ___° counterclockwise from west

Answer 1

start the shopper at (0,0)
After pushing the cart 41 m south, he's now at (0, -41)
After turning west and pushing the cart 28 m, he's now at (-28, -41)

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 (-28, -55)

The distance from the origin is (28^2 + 55^2)^0.5

Let the angle counterclockwise from west be x: then

tan x = 55/28