Vector C = 95 N, 87 degrees W of N. Find the Vertical component

To find the vertical component of a vector given its magnitude and direction, we can use trigonometry.

Given:
- Magnitude of vector \( C = 95 \, \text{N} \)
- Direction of vector \( C = 87^\circ \) west of north

Since the direction is given as "87 degrees west of north," we can visualize this as a vector pointing mostly west but slightly north. The vertical component will be the part of the vector along the north-south axis, and we can calculate it using:

\[
C_{vertical} = C \cdot \cos(\theta)
\]

Where:
- \( C_{vertical} \) is the vertical (northward) component,
- \( C = 95 \, \text{N} \) is the magnitude of the vector,
- \( \theta = 87^\circ \) is the angle measured west of north.

Let's calculate it:

\[
C_{vertical} = 95 \cdot \cos(87^\circ)
\]

Now, I'll compute this.The vertical component of the vector \( C \) is approximately \( 4.97 \, \text{N} \) northward.

Would you like more details or have any further questions?

Here are five related questions to expand on this:

1. How do we calculate the horizontal component of vector \( C \)?
2. What does the horizontal component represent in this case?
3. How do we interpret vectors when the angle is given as "south of east"?
4. How would the calculation change if the direction was "east of north" instead of "west of north"?
5. Can you describe how to break down a vector if it's not aligned with the standard axes?

**Tip:** For any vector, the vertical component always aligns with the y-axis, while the horizontal component aligns with the x-axis.

Vector C = 95 N, 87 degrees W of N. Find the Vertical component.

Learn how to find the vertical component of vector C = 95 N with a direction of 87 degrees west of north. This problem involves trigonometry and vector decomposition, using the formula C_vertical = C * cos(θ). Suitable for students in Grades 10-12.

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