College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 38.5 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 23.5 km/h. How far from Grand Bahama is the hurricane 4.45 h after it passes over the island?
Step 1
Assume that the Grand Bahama Island lies at the origin of the coordinate system shown in the diagram at below. Vector represents the hurricane's displacement at 38.5 km/h and vector represents its displacement after it shifts course three hours later and proceeds at a speed of 23.5 km/h. Vector represents the hurricane's displacement after a total time of 4.45h.
A coordinate plane has a horizontal, leftward axis labeled "west" and a vertical, upward axis labeled "north". Three vectors are plotted.
Vector in the diagram has components to the west and to the north in this coordinate system while vector has only a north component. During the first three hours after passing the island, the displacement of the hurricane is represented by vector , and the storm travels a distance that is the magnitude of . This distance is- Vector A starts at the origin and points up and to the left at an angle of 60.0° above the horizontal axis.
- Vector B, which is much shorter than vector A, starts at the tip of vector A and points vertically upward.
- Vector R starts at the origin and moves up and to the left, ending at the tip of vector B.
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