One of the rectangular components of a force of 50 N is 30 N. The other rectangular component will be

Options

A. 40 N
B. 30 N
C. 35 N
D. 45 N

Explanation

To solve the problem, we need to find the other rectangular component of a force given that one component is 30 N and the resultant force is 50 N. We can use the Pythagorean theorem since the components are perpendicular to each other.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- One rectangular component (F1) = 30 N
- Resultant force (FR) = 50 N

2. **Use the Pythagorean Theorem**:
The relationship between the components and the resultant force can be expressed as:
\[ F_R^2 = F_1^2 + F_2^2 \]
where \( F_2 \) is the other rectangular component we need to find.

3. **Substitute the Known Values**:
Substitute \( F_R \) and \( F_1 \) into the equation:
\[ 50^2 = 30^2 + F_2^2 \]

4. **Calculate the Squares**:
Calculate \( 50^2 \) and \( 30^2 \):
\[ 2500 = 900 + F_2^2 \]

5. **Rearrange the Equation**:
To isolate \( F_2^2 \), subtract \( 900 \) from both sides:
\[ F_2^2 = 2500 - 900 \]
\[ F_2^2 = 1600 \]

6. **Take the Square Root**:
To find \( F_2 \), take the square root of \( 1600 \):
\[ F_2 = \sqrt{1600} = 40 \, \text{N} \]

7. **Conclusion**:
The other rectangular component \( F_2 \) is \( 40 \, \text{N} \).

### Final Answer:
The other rectangular component will be **40 N**.

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