Question

1. An ant crawls on the sidewalk. It first moves South a distance of 8.0 cm. It then turns East and crawls 3.0 cm. 
2. Sketch a vector diagram
3. Distance traveled by the ant is  __ cm.
4. The magnitude of the ant's displacement is __ cm.

Answer 1

(a) Let's sketch a vector diagram:

(b) We can find the distance traveled by the ant as follows:

$$s=s_1+s_2=8.0\ cm+3.0\ cm=11.0\ cm.$$

(c) We can find the magnitude of the ant's displacement from the Pythagorean theorem:

$$d=\sqrt{d_x^2+d_y^2},$$ $$d=\sqrt{(3.0\ cm)^2+(8.0\ cm)^2}=8.54\ cm.$$