Question

Add the following vectors:

440 N at 100 degrees
905 N at 160 degrees

a. 1013.5 N at 149 degrees
b. 1345 N at 130 degrees
c. 1010.4 N at 48.2 degrees
d. 1187.7 N at 141.3 degrees

Answer 1

To add vectors, we calculate the horizontal and vertical components, and then compute the magnitude and direction of the resultant vector, which is approximately 1187.7 N at 141.3 degrees.

Step-by-step explanation:

To add the following vectors, we must break each vector into its horizontal (x-axis) and vertical (y-axis) components using trigonometric functions.

• Vector 1: 440 N at 100 degrees
  Horizontal: 440 N × cos(100°) = -76.396 N
  Vertical: 440 N × sin(100°) = 435.199 N
• Vector 2: 905 N at 160 degrees
  Horizontal: 905 N × cos(160°) = -848.528 N
  Vertical: 905 N × sin(160°) = 311.357 N

Now, add the horizontal and vertical components separately to get the resultant vector:

• Resultant Horizontal: -76.396 N + (-848.528 N) = -924.924 N
• Resultant Vertical: 435.199 N + 311.357 N = 746.556 N

To find the magnitude of the resultant vector (R), use the Pythagorean theorem:

R = √((-924.924 N)2 + (746.556 N)2) = 1187.66 N

Finally, calculate the angle (θ) of the resultant vector with respect to the positive x-axis (east) using the inverse tangent function:

θ = arctan(746.556 N / -924.924 N) = 141.3°

Thus, the resultant vector is approximately 1187.7 N at 141.3 degrees.