The x~component of a sum of vectors is the sum of their x-components. The v-component of a sum of vectors is the sum of their y-components. In fact, this is how you should think about any equation involving vectors. The equation A = B means the x- ._a component of/i. is equal to the x-component of E, and the y-component of}? is equal to the y-component of B. in other words, vector equations are just a shorthand for writing 2 (or 3, if including a z-axis) equations at the same time! Finding Components In physics, we can place our axes in any orientation we choose. 50 the x axis is not always horizontal. You need to be able to nd components no matter how a vector is described and what the axes are. Here's some practice. For each, make a sketch and use trigonometry. 1. A plane ies east northeast at 80 m/s. (If you don't know what "east northeast\" means, google it.) What is the component of its velocity in the direction east? 2. An object falls at terminal velocity (a constant speed) of 30 m/s. Due to a cross-wind, the trajectory is not straight down, but deected south by 10 from vertical. What is the southward component of velocity? 3. A block is released on a frictionless ramp that has an angle of 20\". What is the component of the weight that is down the ramp (parallel to the ramp)? The weight is 10 N. Finding Components without Trigonometry In many situations, it will be easier to find components using the concept of similar triangles, rather than trigonometry. Do the following 3 problems by using similar triangles. Make a sketch. Do not use trigonometry for these problems. (You may use the Pythagorean theorem.) 1. A plane flies from ABQ Sunport to Dodge City Kansas in a straight line. (Ignore the curvature of the Earth.) The distance is 480 miles. Dodge City is 220 miles north and 427 miles east of ABQ. The plane flies at 80 m/s. What is the eastward component of its velocity? 2. An object falls at terminal velocity from 2000 feet up and lands 140 feet south of its start point. Its speed is a steady 30 m/s. What is the southward component of its velocity? 3. A block slides down a frictionless ramp, shown at right. If the block weighs 10 N, what is the component of the weight 5m down the ramp (parallel to it.) 12 m CS Scanned with CamScanner