Question

                         b) Calculate the components of the vector C

1.) The vector A is given by the magnitude |A4.4 cm and the direction with respect to the +1-axis θΑ-140°. The vector B is given by the r-component Bz-4.4 cm and the y-component By3.2 cm

c) Find the magnitude and direction of the vector C

Answer 1

1)

A_x = x-component of $\underset{A}{\rightarrow}$ = |$\underset{A}{\rightarrow}$| Cos$\theta _{A}$ = 4.4 Cos140 = - 3.37 cm

A_y = y-component of $\underset{A}{\rightarrow}$ = |$\underset{A}{\rightarrow}$| Sin$\theta _{A}$ = 4.4 Sin140 = 2.83 cm

B_x = 4.4 cm

B_y = 3.2 cm

C_x = A_x + B_x = - 3.37 + 4.4 = 1.03 cm

C_y = Ay + By = 2.83 + 3.2 = 6.03 cm

c)

using Pythagorean theorem

|C| = sqrt(C_x² + C_y²) = sqrt((1.03)² + (6.03)²) = 6.12 cm

direction : $\theta$ = tan^-1(C_y/C_x) = tan^-1(6.03/1.03) = 80.31 deg