Determine the resultant of the vector sum:
10 N at 045 degrees and then 8N at 068 degrees.
To determine the resultant of the vector sum, we need to find the combined effect of the two vectors given. Here's how you can do it:
Step 1: Convert the vectors into their components.
- The first vector is 10 N at 045 degrees. We can split it into its horizontal (x) and vertical (y) components using trigonometry:
Horizontal component = magnitude * cos(angle)
= 10 N * cos(45°)
= 7.07 N (rounded to two decimal places)
Vertical component = magnitude * sin(angle)
= 10 N * sin(45°)
= 7.07 N (rounded to two decimal places)
- The second vector is 8 N at 068 degrees. Similarly, we can find its components:
Horizontal component = 8 N * cos(68°)
Vertical component = 8 N * sin(68°)
Step 2: Add the horizontal and vertical components separately.
Horizontal component = 7.07 N + (horizontal component of second vector)
Vertical component = 7.07 N + (vertical component of second vector)
Step 3: Convert the resultant components back into magnitude and direction.
- To find the magnitude of the resultant vector, use the Pythagorean theorem:
Magnitude = sqrt((horizontal component)^2 + (vertical component)^2)
- To find the direction of the resultant vector, use the inverse tangent (arctan) function:
Direction = arctan(vertical component / horizontal component)
So, by following these steps, you can calculate the resultant vector.