The resultant of two equal forces acting at right angles to each other is 1414 dyne. Find the magnitude of either force.

Answer

To solve the problem of finding the magnitude of either force when two equal forces act at right angles to each other and their resultant is given as 1414 dyne, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We have two equal forces, \( F_1 \) and \( F_2 \).
- The angle \( \theta \) between them is \( 90^\circ \).
- The resultant force \( R \) is given as \( 1414 \) dyne.

2. **Use the Formula for Resultant of Two Forces**:
- The formula for the resultant \( R \) of two forces \( F_1 \) and \( F_2 \) acting at an angle \( \theta \) is:
\[ R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos \theta} \]
- Since \( F_1 = F_2 = F \) (let's denote the magnitude of either force as \( F \)), and \( \theta = 90^\circ \) (where \( \cos 90^\circ = 0 \)), the formula simplifies to:
\[ R = \sqrt{F^2 + F^2} = \sqrt{2F^2} = F\sqrt{2} \]

3. **Set Up the Equation**:
- We know that \( R = 1414 \) dyne, so we can set up the equation:
\[ 1414 = F\sqrt{2} \]

4. **Solve for \( F \)**:
- To find \( F \), we rearrange the equation:
\[ F = \frac{1414}{\sqrt{2}} \]
- We know that \( \sqrt{2} \approx 1.414 \), so:
\[ F = \frac{1414}{1.414} \]

5. **Calculate the Value**:
- Performing the division:
\[ F = 1000 \text{ dyne} \]

6. **Conclusion**:
- The magnitude of either force \( F_1 \) or \( F_2 \) is \( 1000 \) dyne.

### Final Answer:
The magnitude of either force is \( 1000 \) dyne.