In 2D Cartesian coordinates a vector with magnitude 20 forms

In 2-D Cartesian coordinates, a vector with magnitude 20 forms a 30 degree angle above the positive x-axis. For reference, the negative y-axis represents a 3/2 pi radian angle from the positive x-axis in this coordinate system. By what absolute value percent would the X & Y components of this vector change if the vector\'s magnitude was doubled and the vector was rotated another 110 degrees counter-clockwise?

Solution

Intially the vector is |v| = 20 ; angle = 30 deg

x component = 20cos30 = 10sqrt3

y component = 20sin30 = 10

If the magnitude is doubled 2|v| = 40

angle = 110 +30 = 140 deg

x component = 40cos140 = -15.32

% change in x =100* |-15.32 -10sqrt3|/10sqrt3

= 188.45%

y component = 40sin140 = 25.711

% change in y = 100*|25.711 -10|/10

= 157.11%