Adding Vectors: The “chart thing”

Especially when tutoring physics 12, vector addition comes up.  Let’s use the “chart thing”:

I took Physics 12 in 1988.  In that class, we added vectors component-wise.  However, at university they used sine law and cosine law.  I haven’t seen someone use component-wise addition in over twenty years – until this week.  Now, they call it “the chart thing:)”

Let’s imagine we’re adding the following two vectors:vector 1vector 2

Well, first we use trig to resolve each into horizontal (x) and vertical (y) components:

vector 1 resolvedvector 2 resolved

Now, looking above, we see that for the first vector, the x component is pointing left:  it’s negative.  A downward component would be negative as well, but we don’t have any downward components in this problem.

Now, to the chart:

vector x component y component
vector 1 -12.3 8.60
vector 2 12.0 18.5
total: result vector -0.3 27.1

You just add downwards to get the total x and y components of the resultant vector.  We see that the result has -0.3 for its x component and 27.1 for its y component.  We can build it as follows:

resultant vector
Now, use a² + b² = c² to get the hypotenuse. Of course, you’ll still get 27 (two sig digits), since 0.3 is too small to have any significant effect on the vertical component of 27.1. Use 2ndtan(27.1/0.3) – you may also know it as arctan(27.1/0.3) – to get the angle of 89°.
resultant vector solved

Since there were only two significant digits in the original problem, we should give the answer with two.  (This isn’t always true, technically, but it’s a good rule of thumb.)  Hence, we give the answer in two sig digs: 27 m/s 89° N of W.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.


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