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Lesson: Displacement Vectors

Question Video: Finding the Magnitude and Direction of a Displacement

05:13

Worksheet: Displacement Vectors • 40 Questions

Q1:

In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the day, causing the castaway to lose control of her raft. A search party used satellite images to track her movement from the point that she left the island. Meanwhile a rescue party traveled to intercept her. The following movements were tracked and relayed to the rescue party: north of west for 2.50 km, then south of east for 4.70 km, then south of west for 5.10 km, then east of north for 1.70 km, then south of west for 7.20 km, and finally north of east for 2.80 km. At this point the castaway was rescued.

What was the magnitude of the displacement of the castaway from the point she left the island to the point where she was rescued?

What was the direction of the castaway’s displacement from the point she left the island to the point where she was rescued?

Q2:

Three displacement vectors , , and have magnitudes of 10.0 cm, 7.0 cm, and 8.0 cm respectively. The directions of , , and make counterclockwise angles of , , and respectively with the positive -axis, as shown in the diagram. The vector sum , the vector sum , and the vector sum .

Find the magnitude of .

Find the counterclockwise angle that the direction of makes with the positive -axis.

Find the magnitude of .

Find the counterclockwise angle that the direction of makes with the positive -axis.

Find the magnitude of .

Find the counterclockwise angle that the direction of makes with the positive -axis.

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  • E

Q3:

A farmer wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as , , and in the diagram. He then correctly calculates the length and orientation of the fourth side, .

What is his result for the length of side ? Give your answer in kilometers.

What is his result for angle in degrees?

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