![]() ![]() If one of the vectors to be added is not directed due east, west, north or south, then vector resolution can be employed in order to simplify the addition process. Resolving an Angled Vector into Right Angle Components Use this video to learn more about Adding Right Angle Vectors. The mnemonic SOH CAH TOA can help one remember how the lengths of the opposite, adjacent and hypotenuse sides of the right triangle are related to the angle value. The angles within the right triangle can be determined from knowledge of the length of the sides using trigonometric functions. The Pythagorean theorem can be used to relate the magnitude of the hypotenuse to the magnitudes of the other two sides of the triangle. Two vectors that are added at right angles to each other will sum to a resultant vector that is the hypotenuse of a right triangle. This video explains more about the Graphical Method of Vector Addition. The diagram becomes an important tool in the solution of the problem. In this set of problems, you will have to be able to read the word story problem and sketch an appropriate vector addition diagram. The resultant is equivalent to the sum of the individual vectors. The resultant vector is then drawn from the tail of A (starting point) to the head of B (finishing point). If adding vector B to vector A, then vector A should be drawn first then vector B should be added to it by drawing it so that the tail of vector B starts at the location where the head of vector A ends. Such individual displacement vectors can be added using a head-to-tail method of vector addition. For instance, a person in a maze makes several individual displacements in order to finish some distance out of place from the starting position. Often times a motion involves several segments or legs. This video on the Direction of Vectors will provide much help on understanding direction conventions. The direction of a vector is represented as the counter-clockwise angle of rotation which the vector makes with due East. One convention commonly used for expressing the direction of vectors is the counter-clockwise from east convention (CCW). When a vector is neither north or south or east or west, an additional convention must be used. In Physics, we utilize the map convention to express the direction of a vector. On a map, up on the page is usually in the direction of North and to the right on the page is usually in the direction of east. Most of us are familiar with the map convention for the direction of a vector. The direction can be described as being east, west, north, or south using the typical map convention. Problems range in difficulty from the very easy and straight-forward to the very difficult and complex.ĭirection: The Counter-Clockwise From East ConventionĪ vector is a quantity that has magnitude and direction. The problems target your ability to perform basic vector operations such as vector addition and vector resolution, to use right angle trigonometry and vector addition principles to analyze physical situations involving displacement vectors, and to combine a conceptual understanding of projectile motion with an ability to use kinematic equations in order to solve horizontally and non-horizontally launched projectile problems. There are 17 ready-to-use problem sets on the topic of Vectors and Projectiles. Vectors and Projectiles: Problem Set Overview ![]()
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