Displacement Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
A car drives 3 km north, then 4 km east. What is the magnitude of the total displacement?

Solution

  1. 1
    Step 1: North displacement is (0,3)(0, 3) and east displacement is (4,0)(4, 0), so total displacement vector =(4,3)= (4, 3).
  2. 2
    Step 2: Magnitude =42+32=16+9=25=5= \sqrt{4^2 + 3^2} = \sqrt{16+9} = \sqrt{25} = 5 km.

Answer

5 km
The two legs of the trip are perpendicular, forming a right triangle with legs 3 and 4. The displacement is the hypotenuse = 5 km. The total distance driven was 7 km, but the straight-line displacement from start to finish is only 5 km.

About Displacement

The straight-line change in position from start to end, with both a distance and a direction.

Learn more about Displacement →

More Displacement Examples

Example 1 easy

A person walks 5 m east and then 5 m west. What is their displacement?

Example 2 medium

A robot moves from point [formula] to point [formula]. Find the displacement vector and its magnitud

Example 4 hard

A particle undergoes three displacements: [formula], [formula], [formula]. Find the net displacement

← All Displacement Examples Displacement Concept