8 Component VectorsVisualizing Vectors in 2 Dimensions | Mechanics | Khan AcademyVector resolutionBreaking a vector into the x- and y- componentsRx =Ry =vector R =Rx = the x component of a vector, RRy = the y component of a vector, R
9 ExampleFind the x- and y-component of R if R = 15 cm andө = 50˚.
10 Adding Vectors by Components Add the vectors.15 m/s13 m/s20˚40˚
17 ExampleThe table below represents a set of force vectors. These vectors begin at the origin of a coordinate system, and end at the coordinates given in the table.What is the magnitude of the resultant of the sum of these three vectors?What is the size of the angle, ө, that the resultant makes with the horizontal (x-axis)?Vector #x-value (N)y-value (N)A0.06.0B5.0C-10.0
22 ExampleA GPS receiver indicates that your home is 15.0 km and 40.0˚ north of west, but the only path through the woods leads directly north. If you follow the path 5.0 km before it opens into a field, how far, and in what direction, would you have to walk to reach your home? *north of west = north from west
23 Ax = 0 Bx Rx = 15 cos 140˚ = - 11.5 Ay = 5 By Ry = 15 sin 140˚ = 9.6 x km, Bө ˚R, 15 km5 km, A40˚Ax = 0BxRx = 15 cos 140˚ =Ay = 5ByRy = 15 sin 140˚ = 9.6Ax + Bx = Rx0 + Bx =Bx =Ay + By = Ry5 + By = 9.6By = 4.6
24 Ay + By = Ry Ax + Bx = Rx 5 + By = 9.6 0 + Bx = - 11.5 By = 4.6 vectorsx component (km)y component (km)A5BBxByR15 cos 140˚ =15 sin 140˚ = 9.6x km, Bө ˚4.6 kmkmAy + By = Ry5 + By = 9.6By = 4.6Ax + Bx = Rx0 + Bx =Bx =x =ө + 90˚ = cos-1 (-11.5/12.4) =158˚ө = 158˚ - 90˚ = 68˚
25 ExampleA football player runs directly down the field for 35 m before turning an additonal 15 m before getting tackled. What is the magnitude and direction of the runner’s total displacement?