Question

Add the following vectors using head-to-tail method and verify your results using the component method.

Answer 1

Answer:

See attached image for the requested graphs.

Part 1 : Vector sum is about 9.4 cm long in the graph, from components: about 9.35 cm long. Percent difference = 0.5%

Part 2: Vector sum is about 7.6 cm long in the graph and from components: 7.57 cm long. Percent difference = 0.4%

Explanation:

Part 1.

The graphical addition of the three vectors A, B and C gives a vector sum of approximately 9.4 cm at an angle of about 84 degrees

The component form addition is

Ax + Bx + Cx  = 3.5 + 0 + (-2.5)  = 1

Ay + By + Cy  = 2.0 + 3 + 4.3  = 9.3

Magnitude: $\sqrt{1^2+9.3^2} \approx 9.35\,\,cm$

The percent difference is: (9.4-9.35) * 100 /9.35 = 0.5%

Part 2.

The graphical addition of the four vectors (A, B, C, and D) measures approximately  7.6 cm at an angle of about 124 degrees.

The component form addition is

Ax + Bx + Cx + Dx = 3.5 + 0 + (-2.5) + (-5.2) = -4.2

Ay + By + Cy + Dy = 2.0 + 3 + 4.3 + (-3) = 6.3

Magnitude = $\sqrt{(-4.2)^2+6.3^2} \approx 7.57\,\,cm$

The percent difference is: (7.6-7.57) * 100 /7.57 = 0.4%