TP 3.19

A = 5.00  @ -90.0^o

B = 10.0  @ 0^o

A_x = A cos(q_A) = (5.00) cos(-90.0^o) =  0

  A_y = A sin(q_A) = (5.00 ) sin(-90.0^o) = -5.00

  B_x = B cos(q_B) = (10.0 m) cos(0^o) = 10.0

 B_y = B sin(q_B) = (10.0 m) sin( 0^o) = 0

  (a) R_x = A_x + B_x = (0 ) + (10.0) = 10.0

       R_y = A_y + B_y = (-5.00 ) + (0) = -5.00 

       R = ( R_x² + R_y²)^1/2 = ( (10.0 )² + (- 5.00 m)²)^1/2 = 11.2

       q_R = tan^-1 (R_y/R_x) =  tan^-1 ((-5.00 )/(10.0 )) = -26 .6^o

(b) R_x = A_x - B_x = (0 ) - (10.0) = -10.0

       R_y = A_y - B_y = (-5.00 ) - (0) = -5.00 

       R = ( R_x² + R_y²)^1/2 = ( (-10.0 )² + (- 5.00 m)²)^1/2 = 11.2

       q_R = tan^-1 (R_y/R_x) =  tan^-1 ((-5.00 )/(-10.0 )) = 26 .6^o+ 180^o = 207^o

(c) R_x = B_x - A_x = (10.0) - (0) = 10.0

       R_y = B_y - A_y = (0 ) - (-5.00) = 5.00 

       R = ( R_x² + R_y²)^1/2 = ( (10.0 )² + (5.00 m)²)^1/2 = 11.2

       q_R = tan^-1 (R_y/R_x) =  tan^-1 ((5.00 )/(10.0 )) = 26 .6^o