Question

A vector has a magnitude of 40.0 units and points 35.0° above the positive x axis. A second vector has a magnitude of 65.0 units and points in the negative x direction. Use the component method of vector addition to find the magnitude and direction,

Answer 1

Answer: 39.6 units

Explanation:

F1:

x-component: 40cos35 = 32.7

y-component: 40sin35 = 22.9

F1 = (32.7)i + (22.9)j

F2:

x-component: -65cos0= -65

y-component: -65sin0 = 0

F2 = (-65)i

Now add the forces using their components.

F1 + F2 = (32.7)i + (22.9)j + (-65)i = (-32.3)i + (22.9)j

To find the magnitude of the vector, r, use the Pythagorean theorem.

r = √((-32.3)^2 + (22.9)^2) = 39.6 units

To find the angle, use the inverse tangent function (arctan).

θ = arctan(22.9 / -32.3) = -35°

90 + 35 = 125°

The -35 depicts a triangle in the fourth quadrant of the unit circle. Using vertical angles, you'd see that the angle of the vector is 90-35=55° north of west. Relative to the positive x-axis, this would be a 125° angle.

Answer 2

Answer:

Magnitude = 39.64units

Direction = 54.65°

Explanation:

The magnitude of the component vectors is the a single force that replaces all the forces acting in space and this single vector is known as the resultant.

Find the solution to the problem in the attachment.