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Question

a car goes 5.0 km east, 3.0 km south, 2.0 km west and 1 km north. (a) Determine how far north and how far east it has been displaced. (b) Find the displacement of the vector both graphically and algebraically

Answer 1

Let the displacements in the north and east directions be positive and the west and south directions be negative.

We algebraically add all north and south distances and all east and west distances.

+ 5.0 east - 2.0 west = 3.0 km east

-3.0 south + 1.0 north = -2.0 km south.

The displacement is the resultant of the final directions obtained using the Pythagorean theorem.

D² = 3.0² -2.0² = 13 , D = √13 = 3.6 km from the starting point in the direction 3.0 km east and 2.0 km south of the starting point.

To do this graphically, draw the individual displacements head to tail on the graph, then connect the tail of the starting point to the head of the final displacement arrow.