Chapter 3, Problem 8PQ

The layout of the town of Popperville is a perfectly square grid, with blocks 100 feet long (Fig. P3.8). A cat leaves her house and travels to Mike Mulligan’s place 4 blocks west and 3 blocks north of its starting point. After lapping up the milk that Mike always leaves out, the cat travels an additional 1 block north and 3 blocks east to Mrs. McGillicutty’s house.

a. On your paper, carefully copy the grid of streets that contains the cat’s house, Mike Mulligan’s house, and Mrs. McGillicutty’s house. Then draw and label three displacement vectors on your sketch: $\Delta {\stackrel{\to }{r}}_1$, the cat’s displacement from her house to Mike Mulligan’s; $\Delta {\stackrel{\to }{r}}_2$, the cat’s displacement from Mike Mulligan’s to Mrs. McGillicutty’s; and $\Delta {\stackrel{\to }{r}}_{\text{tot}}$, the cat’s total displacement.

b. Write an equation to relate the three displacement vectors you have drawn.

c. Is the distance the cat traveled greater than, less than, or equal to the magnitude of the cat’s total displacement vector? Explain.

FIGURE P3.8