Find magnitude of the resultant force if the component is + 129.9 N and the y component is + 75 N

To find the magnitude of the resultant force when the components are given, we can use the Pythagorean theorem, as the resultant force \( F \) is the hypotenuse of a right triangle formed by its \( x \)- and \( y \)-components.

Given:
- \( F_x = +129.9 \, \text{N} \)
- \( F_y = +75 \, \text{N} \)

The formula for the magnitude of the resultant force \( F \) is:
\[
F = \sqrt{F_x^2 + F_y^2}
\]

Substituting the values:
\[
F = \sqrt{(129.9)^2 + (75)^2}
\]
\[
F = \sqrt{16842.01 + 5625}
\]
\[
F = \sqrt{22467.01}
\]
\[
F \approx 149.89 \, \text{N}
\]

### Answer:
The magnitude of the resultant force is approximately \( 149.89 \, \text{N} \).

Would you like a detailed explanation of the Pythagorean theorem or any other related concepts?

Here are five related questions to explore this topic further:

1. How do we calculate the direction of the resultant force with respect to the \( x \)-axis?
2. What would the magnitude of the resultant be if the \( y \)-component were negative?
3. How does this approach change for three-dimensional forces with \( z \)-components?
4. What happens to the magnitude if both \( x \) and \( y \)-components double?
5. What is the effect of changing the \( x \)-component only on the resultant’s magnitude?

**Tip:** Always check whether forces are perpendicular when applying the Pythagorean theorem to find the resultant.

Find magnitude of the resultant force if the x component is + 129.9 N and the y component is + 75 N.

Calculate the magnitude of the resultant force with an x-component of +129.9 N and a y-component of +75 N. Using the Pythagorean theorem, learn how to solve for the hypotenuse in this vector problem. Suitable for high school physics and math students.

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