Position & Displacment :: | :: Adding on a Straight line

Almost everything in motion will change its direction or movement pattern. Cars can swerve, surfers twist and turn; these are such examples of movement. The resultant displacement on a angle can be different form the actual distance travelled. Even the most complex systems of movement can be depicted on a vector diagram, which is why Oliver Heaviside invented the vector diagram. The resultant displacement and the distance travelled can be totally different.

If you look at the above the picture you can see that the resultant displacement will be different from the total distance the yellow raft will travel. To find the resultant displacment you must have the direction, and distance travelled.

Direction

Direction is a very important aspect of investigating vectors. We use a common convention of direction, the compass. If a direction does not exactly match a direction on the compass then we write it as a angle from the closest compass point. To measure the angle exactly you must use a protractor. The direction can be written as [30o E of N]. The diagram for this description can look like the following:

Adding Two-Dimensional Vectors using Scale Diagrams

If you know the size and direction of each displacement then we can draw a scale diagram in order to obtain the resultant displacement.

 Sample Cindy decided she wanted to visit her friend Kelvin. She decides to take a bus 30 km south to a near by street. She then walked 10 km west to his house. What is the resultant displacement? 1 cm = 10 km 1 = 30 km [S] 2 = 10 km [W] r = ? This drawing was not created accurately, but it provides a example for this question. (you might try drawing this out on a piece of graph paper) If you measure this out, you will get a displacement of 32 m [70o west of south]