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Topic #8: X and Y COMPONENTS of VECTORS In example M on the last handout, you found the resultant force vector for this: “A force of 100n North and 100n East acting on the same object: find their resultant, FR.” The answer was: FR = 141newtons NorthEast But what do you call the other two vectors, namely the 100n North and 100n East vectors that combined to make the resultant? These are called the COMPONENTS of FR, and in your diagram are the legs of the triangle formed, while FR is the hypotenuse. 100n East is Fx, the horizontal or X component, and 100n North is Fy, the vertical or Y component. Remember their vector sum is not 200n; FR was found by the Pythagorean Theorem and the angle’s tangent. In example N: “A rower’s velocity of 3 km/hr West: find their resultant, The answer was: VR = 5 km/hr @< 37º resultant velocity has two components, VY = 4 km/hr South? of 4 km/hr South and a river’s current VR.” West of South Do you see that this namely, VX = 3 km/hr West and Often the value of a vector, its magnitude and direction, is known or given in a problem, but the question is to find the X and Y components of the vector. This is the opposite process from finding a resultant vector. The Mathematical Solution Method: Make a vector triangle, and use the sine and cosine functions to find the Y and X components of a known vector. A carefully plotted diagram, done to scale, also allows you to measure the two components when using the graphical solution method. For each example below, draw a vector diagram and find the vector’s X and Y components. Use the mathematical method. (We will also practice the graphical method in class for (C) and (E) below, and compare the answers obtained by the two different methods.) A) An applied force of 100n North B) A car’s velocity of 30 km/hr East C) A walk of 20m Northeast D) A Displacement of 5km Southwest E) A force of 50n @ <60ºS of E F) A plane’s velocity = 10m/s @ <30ºE of N