Adding Vectors by Components Example # 2

In this example, we are given that a certain car takes a three day trip and travels the abovementioned distances during the three day trip. What we want to find is the final displacement (both magnitude and direction) of the car after the three day trip. We are essentially breaking down each vector (one vector per day) into their component vectors that point along the x and y directions. We are then summing up all the vectors that point along x axis as well as all the vectors that point along the y axis. Note that going upward along the y axis and towards the right along the x axis is chosen to be positive. After calculating the component vectors of our resultant vector, we are ready to use the formula to determine the magnitude as well as the direction. To obtain the magnitude, we sum up the squares of both component vectors and then take the square root and round off to three significant digits. In order to find the direction (angle), we need to determine the value of the ratio of the magnitude of y component vector to the magnitude of the x component vector. We then take the inverse tangent function of that value and obtain the value of the angle that corresponds to the direction of the resultant vector.

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