A shopper pushes a cart 50 m south down one aisle and then turns 90.0° west and moves 12 m. He then makes another 90.0° turn and moves 20 m. What is the largest possible displacement of the shopper?

if his last turn is to the south

he will be 70 m S and 12 m W of his starting position

use Pythagoras to find the displacement

To find the largest possible displacement of the shopper, we need to calculate the resultant displacement.

Step 1: Calculate the displacement in the x-direction (east/west).
The shopper initially moves 50 m south, which means there is no displacement in the x-direction.

Step 2: Calculate the displacement in the y-direction (north/south).
After turning 90.0° west, the shopper moves 12 m. This adds a displacement of -12 m in the y-direction.

Step 3: Calculate the resultant displacement using the Pythagorean theorem.
The resultant displacement can be calculated as the square root of the sum of the squares of the displacements in the x and y directions:
Resultant Displacement = √(Displacement_x^2 + Displacement_y^2)

In this case, Displacement_x = 0 m and Displacement_y = -12 m. Therefore:
Resultant Displacement = √(0^2 + (-12)^2)
= √(0 + 144)
= √144
= 12

Therefore, the largest possible displacement of the shopper is 12 meters.