Question

The three displacement vectors in the drawing have magnitudes of A = 5.05 m, B = 4.90 m, and C = 4.20 m. Find the resultant (magnitude and directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above or below the positive or negative x axis. (Assume α = 25° and β = 61°. Give an answer between 0 and 90°.)

Answer 1

given A = 5.05 m ,B = 4.90 m , C = 4.20 m

A_x = - A cos 25°

= - 5.05 X cos25°

= - 4.577 m

A_y = A sin25°

= 5.05 X 0.423

= 2.13 m

B_x = B cos61°

= 4.90 X 0.485

= 2.376 m

B_y = B sin61°

= 4.9 X 0.875

= 4.286 m

C_x = C X cos90

= 4.20 X cos 90

= 0 m

C_y = -C X sin90

= - 4.20 X 1

= -4.20 m

now in x - direction

total is A_x + B_x + C_x = -4.577 + 2.376 + 0 = - 2.20 m

same way in y - direction

A_y + B_y + C_y = 2.13+ 4.286 - 4.20 = 2.216 m

to find the magnitude

= (2.20)² + (2.216)²

magnitude = 3.122 m

the angle is = tan^-1 ( y / x )

= tan^-1 (2.216 / 2.20 )

= 45.20° and in direction in negative X - axis

Please rate my answer, good luck..