Physics

A shopper pushes a cart 50 m south down one aisle and then turns 90.0° west and moves 19 m. He then makes another 90.0° turn and moves 13 m.

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

Could you show me step by step

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1. 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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