Adding Vectors at an Angle
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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 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.
Adding Two-Dimensional Vectors Algebraically
Using algebra to add two-dimensional vectors together is more complicated that using it for one-dimensional vectors; in fact you have to use the method for adding one-dimensional vectors within this method. Essentially, what you have to do is differentiate the vertical vectors from the horizonal vectors, add them together (respectively), and come up with two resultant vectors (one vertical and one horizonal). Apply the Pythagorean theorum to these to find the distance compontent of the final vector, and divide them to find the slope of the final vector (which can be converted to degrees as the direction of the final vector). If the vector has both a vertical and horizontal component, you have to use its slope to isolate these components.
However, adding two-dimensional vectors algebraically is not a grade 10 topic and will therefore not be covered in detail here; this summary is just meant to prepare you for the rest of high school.
Continue to the next lesson: Velocity