Classical Mechanics

Vector Kinematics

Total displacement of a set of displacement vectors


A boy walks 8 km8 \text{ km} west, then 3 km 3 \text{ km} south, and then 3 km 3 \text{ km} east. Determine his net displacement.

Let +i^ +\hat{i} be the unit vector for east, and +j^ +\hat{j} be that for north.

Caitlyn is walking around the campus. She walks 100 meters 100 \text{ meters} north, then 300 meters 300 \text{ meters} east, and at last 200 meters 200 \text { meters} north. Now, how far is she from her initial position?

Two helicopters take off from the same landing area. One helicopter proceeds 82 km 8\sqrt{2} \text{ km} due southwest. The second flies 4 km 4 \text{ km} east. Determine the final position of the second helicopter with respect to the first.

A A is the vector sum of the two vectors: (5i^3j^+2k^) (5 \hat{i} - 3 \hat{j} + 2 \hat{k} ) and (i^+5j^+6k^). ( \hat{i} + 5 \hat{j} +6 \hat{k} ). What is vector A A in unit vector notation?

A girl walks 600 m600 \text{ m} east, then 1 km 1 \text{ km} south, and then 5 km 5 \text{ km} east. Find her total displacement.

+i^ +\hat{i} is the unit vector for east, and +j^ +\hat{j} is that for north.


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