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.

Question

(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

Answer 1

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