Vector A has magnitude of 9.77 units and points due east. Vector B points due north.
1) What is magnitude of B, if the vector A+B points 34.7 north of east?
2) Find magnitude of A+B
I am not sure what formulas to use for this. If someone could show me how to start this I will try to solve it myself and then check back to see if I am correct. Thank you!
tanα =B/A,
B =A•tanα = 9.77•tan34.7º =6.77.
cosα = A/(A+B),
(A+B) = A/ cosα = 9.77/cos34.7º = 11.88
Thank you!!
To solve these problems, we can use vector addition and trigonometry. Let's break it down step by step:
1) What is the magnitude of B, if the vector A+B points 34.7 degrees north of east?
To find the magnitude of vector B, we need to consider the direction of the resultant (A+B) vector. Since vector B points due north, and the resultant vector points 34.7 degrees north of east, we can consider the triangle formed by vector A, vector B, and the resultant vector.
To solve for the magnitude of B, we need to find the component of the resultant vector that is in the north direction (parallel to vector B).
We can use trigonometry to find this component. The magnitude of vector B is given by:
|B| = |A+B| * sin(θ)
where θ is the angle between vector A+B and vector B.
In this case, θ is 34.7 degrees, which means we need to find sin(34.7 degrees).
Using a calculator, we can find that sin(34.7 degrees) is approximately 0.571.
Therefore, the magnitude of vector B can be calculated as:
|B| = 9.77 * 0.571
Now, you can calculate |B| and check your answer.
2) Find the magnitude of A+B:
To find the magnitude of A+B, we need to use vector addition.
The magnitude of the resultant vector can be found using the Pythagorean theorem:
|A+B| = √(Ax+Bx)^2 + (Ay+By)^2
where Ax and Ay are the x and y components of vector A, and Bx and By are the x and y components of vector B.
Since vector A points due east, the x component of vector A is equal to its magnitude (9.77 units). The y component is 0 since it points east.
Vector B points due north, so its x component is 0, and its y component is the magnitude of vector B (which you previously calculated in step 1).
Using these values, you can calculate the magnitude of A+B using the formula above.