need a step by step process of combining this question into one vector:
56 NEWTONS at 296 degrees, then 83 newtons at 152 degrees
To combine the two given vectors into one vector, you need to resolve the vectors into their horizontal and vertical components, add the horizontal components together, and add the vertical components together. Here is the step-by-step process:
Step 1: Resolve the first vector (56 Newtons at 296 degrees) into its horizontal and vertical components.
- The horizontal component is given by: 56 Newtons * cos(296 degrees)
- The vertical component is given by: 56 Newtons * sin(296 degrees)
Step 2: Resolve the second vector (83 Newtons at 152 degrees) into its horizontal and vertical components.
- The horizontal component is given by: 83 Newtons * cos(152 degrees)
- The vertical component is given by: 83 Newtons * sin(152 degrees)
Step 3: Add the horizontal components together.
- Add the horizontal component from the first vector to the horizontal component from the second vector.
Step 4: Add the vertical components together.
- Add the vertical component from the first vector to the vertical component from the second vector.
Step 5: Use the horizontal and vertical components to calculate the magnitude (length) and direction of the combined vector.
- The magnitude is given by the square root of (horizontal component squared + vertical component squared).
- The direction is given by the arctan of (vertical component / horizontal component), converted from radians to degrees.
To summarize, follow these steps:
1. Resolve the first vector into horizontal and vertical components.
2. Resolve the second vector into horizontal and vertical components.
3. Add the horizontal components together.
4. Add the vertical components together.
5. Calculate the magnitude and direction of the combined vector using the horizontal and vertical components.
By following these steps, you can combine the given vectors into one vector.