Adding Vectors by Components Example # 1

Suppose that a person decides travel 25.0 kilometers upward along the y axis. They then make a right turn (60 degrees with respect to the x axis in the clockwise direction) and travel for 50.0 more kilometers. We need to add up these two vectors to determine the final resultant vector that will tell us the displacement of our person from their initial position. Instead of using the tedious graphical methods, we shall add the vectors using their individual component vectors. In the first part of the problem, our goal is to determine what the individual x and y component vectors are of the two vectors are. We then sum up all the x component values and y component values. In the next part, we use the formula to determine the magnitude as well as direction of the final resultant vector. We find that our persons final position is located 31.0 kilometers away from the initial point and the vector points at an angle of 36.6 below (clockwise) the x axis.

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