As our first example, consider the following vector addition problem: Example 1: A student drives his car 6.0 km, North before making a right hand turn and driving 6.0 km to the East. Finally, the student makes a left hand turn and travels another 2.0 km to the north. What is the magnitude of the overall displacement…
Earlier in this lesson, we learned that vectors oriented at right angles to one another can be added together using the Pythagorean theorem. For instance, two displacement vectors with magnitude and direction of 11 km, North and 11 km, East can be added together to produce a resultant vector that is directed both north and east. When the…
The trigonometric method of vector resolution involves using trigonometric functions to determine the components of the vector. Earlier in lesson 1, the use of trigonometric functions to determine the direction of a vector was described. Now in this part of lesson 1, trigonometric functions will be used to determine the components of a single vector. Recall from…
The parallelogram method of vector resolution involves using an accurately drawn, scaled vector diagram to determine the components of the vector. Briefly put, the method involves drawing the vector to scale in the indicated direction, sketching a parallelogram around the vector such that the vector is the diagonal of the parallelogram, and determining the magnitude…
As mentioned earlier in this lesson, any vector directed at an angle to the horizontal (or the vertical) can be thought of as having two parts (or components). That is, any vector directed in two dimensions can be thought of as having two components. For example, if a chain pulls upward at an angle on the…
A vector is a quantity that has both magnitude and direction. Displacement, velocity, acceleration, andforce are the vector quantities that we have discussed thus far in the Physics Classroom Tutorial. In the first couple of units, all vectors that we discussed were simply directed up, down, left or right. When there was a free-body diagram depicting the forces acting upon an object, each individual force…
The resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together. If displacement vectors A, B, and C are added together, the result will be vector R. As shown in the diagram, vector R can be determined by the use of an accurately drawn, scaled, vector addition diagram. To…
The magnitude and direction of the sum of two or more vectors can also be determined by use of an accurately drawn scaled vector diagram. Using a scaled diagram, the head-to-tail method is employed to determine the vector sum or resultant. A common Physics lab involves a vector walk. Either using centimeter-sized displacements upon a map or meter-sized displacements…
The measure of an angle as determined through use of SOH CAH TOA is not always the direction of the vector. The following vector addition diagram is an example of such a situation. Observe that the angle within the triangle is determined to be 26.6 degrees using SOH CAH TOA. This angle is the southward angle of…
The direction of a resultant vector can often be determined by use of trigonometric functions. Most students recall the meaning of the useful mnemonic SOH CAH TOA from their course in trigonometry. SOH CAH TOA is a mnemonic that helps one remember the meaning of the three common trigonometric functions – sine, cosine, and tangent functions. These…