The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated.
DATA: α= 45.9o β= 57.6o |A| = 7.9 cm. The vector A - B is parallel to the -x axis (points due West). Calculate the magnitude of the vector A+B. I found all the sides of the triangles made my each vector, and then using the equation sqrt(a+c)^2+(b+d)^2 i got 17.50 as an answer. What did i do wrong?
To find the magnitude of the vector A+B, you can use vector addition. However, it seems like there might be an error in your calculation.
Here's the correct approach:
1. Start by breaking down vector A into its x and y components. The x-component (Ax) can be found using the formula Ax = |A| * cos(α). Similarly, the y-component (Ay) can be found using Ay = |A| * sin(α). In this case, |A| = 7.9 cm and α = 45.9°, so you can calculate Ax and Ay.
2. Next, break down vector B into its x and y components using the same approach. The angles might be different, so use the given angle β and the magnitude of vector B to find its x and y components.
3. To find the x-component of A+B, you subtract the x-component of B from the x-component of A: Ax+B = Ax - Bx. Since the vector A-B is parallel to the -x axis (pointing due West), its x-component would be the negative of Bx.
4. Similarly, to find the y-component of A+B, subtract the y-component of B from the y-component of A: Ay+B = Ay - By.
5. Now that you have the x and y components of A+B, you can calculate the magnitude using the formula |A+B| = sqrt((Ax+B)^2 + (Ay+B)^2). Make sure to use the correct signs for the x and y components.
Follow these steps to recalculate the magnitude of A+B and ensure you have taken into account all the correct signs and calculations.