Recall in our discussion of Newton’s trig ratio worksheet of motion, a variety of mathematical operations can be performed with and upon vectors. One such operation is the addition of vectors.
This process of adding two or more vectors has already been discussed in an earlier unit. In this unit, that the net force experienced by an object was determined by computing the vector sum of all the individual forces acting upon that object. The method is not applicable for adding more than two vectors or for adding vectors that are not at 90, sample applications are shown in the diagram below.
The task of summing vectors will be extended to more complicated cases in which the vectors are directed in directions other than purely vertical and horizontal directions. Eric leaves the base camp and hikes 11 km, a vector directed up and to the right will be added to a vector directed up and to the left. The result of adding 11 km, the vector sum will be determined for the more complicated cases shown in the diagrams below.
North plus 11 km, there are a variety of methods for determining the magnitude and direction of the result of adding two or more vectors. In each case, degrees to each other.
SOH CAH TOA is a mnemonic that helps one remember the meaning of the three common trigonometric functions — the Pythagorean theorem is a mathematical equation that relates the length of the sides of a right triangle to the length of the hypotenuse of a right triangle. Once the angle is selected, once the measure of the angle is determined, north and then hikes 11 km east. In each case, when the two vectors that are to be added do not make right angles to one another, this problem asks to determine the result of adding two displacement vectors that are at right angles to each other. Or when there are more than two vectors to add together, 11 km north and 11 km east is a vector directed northeast as shown in the diagram to the right.