1. Vector B is in the third quadrant, therefore its x and y components are negative.
If B's direction is 218 degrees (counter clockwise from the positive x-axis) then which expression best describes B's x-component?
1. B*sin(38)
2. B*cos(38)
3. B*tan(38)
4. B*cos(218)
5. B*tan(218)
6. B*sin(218)
2. There is a vector H with x component = -250[g] and y component = 70[g].
What is the magnitude of H?
1) 4. B*cos(218)
2) sqrt [(250)^2 + (70)^2]= 259.6
For question 1, we need to find the x-component of vector B given its direction of 218 degrees. To do this, we can use the cosine function as it gives us the ratio of the adjacent side (which represents the x-component) to the hypotenuse (which represents the magnitude of vector B).
Since vector B is in the third quadrant, both its x and y components will be negative. Therefore, the expression that best describes B's x-component is option 4, B*cos(218).
For question 2, we need to find the magnitude of vector H given its x and y components. To do this, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.
Using the given x and y components (-250[g] and 70[g]), we can calculate the magnitude of vector H as follows:
Magnitude of H = sqrt[(x component)^2 + (y component)^2]
= sqrt[(-250[g])^2 + (70[g])^2]
= sqrt[62500[g^2] + 4900[g^2]]
= sqrt[67400[g^2]]
≈ 259.6
Therefore, the magnitude of vector H is approximately 259.6[g].