Sue travels 10 miles north, 3 miles east, 7 miles south, 2 miles west, 1 mile north, 1 mile west, and 4 miles south. a. Draw the motion. b. What is her displacement? c. What is her distance?

Answer 1

These types of questions are easily answered with some graph paper if you find yourself struggling with visualizing what is happening. First, you need to know the cardinal directions (compass, N, S, E, W). Remember North is up, South is down, and it spells the word "we" as you go across.

A) So Sue goes up 10, right 3, down 7, left 2, up 1 more, left 1 more, and down 4 more. On graph paper, this is easily drawn (label each segment of the path so your teacher knows you understood the motion correctly in the order that Sue traveled).

B) For displacement, the goal is to see how far Sue moved from her initial position. To do this, we will "cancel out" any up movements with down movements and will do the same for any left movements with right movements:

Up movements: 10 north plus 1 north (11 up total)

Down movements: 7 south plus 4 south (11 down total)

She has not moved either up or down, since they cancel out.

Left movements: 2 west plus 1 west (3 west total)

Right movements: 3 east (total)

She has not moved either left or right, since they cancel out.

This means Sue did a lot of walking, but came back to where she started. Her displacement is zero miles.

C. Distance is what your Fitbit/SmartWatch would show that you had walked along the way - so all we do here is total up all of the miles she walked: 10 + 3 + 7 + 2 + 1 + 1 + 4 = 28 miles total.