Let ? be the angle that the vector makes with the + x -axis, measured counterclockwise from that axis. Find angle ? for a vector that has these components: (a) Ax = 2.00 m, Ay = - 1.00 m; (b) Ax = 2.00 m, Ay = 1.00 m; (c) Ax = - 2.00 m, Ay = 1.00 m; (d) Ax = - 2.00 m, Ay = - 1.00 m.
Solution 30E Any vector quantity in two dimension can be written as A = A ix+ A jyˆ Where i is the unit vector along x and j is the unit vector along y axis. If A making an angle with +x axis, then we can write that A x |A|cos ……(1) And A y |A|sin …….(2) Here |A| is the magnitude of the vector. Now dividing (2) with (1) we get Ay A = tan x A = tan ( ) y Ax Step 1 a) Here we have A x 2.00 m A y 1.00 m Hence the angle is A = tan ( ) = tan ( 1 1.00 m) = 26.6° Ax 2.00 m