The horizontal and vertical components of a force are 8 N and 15 N respectively. The force is

Options

A. 23 N
B. 20 N
C. 17 N
D. 7 N

Answer

To find the resultant force when given the horizontal and vertical components, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components**:
- Horizontal component (F_x) = 8 N
- Vertical component (F_y) = 15 N

2. **Use the Pythagorean Theorem**:
The magnitude of the resultant force (R) can be calculated using the formula:
\[ R = \sqrt{F_x^2 + F_y^2} \]

3. **Calculate the Squares of the Components**:
- Calculate \( F_x^2 \):
\[ F_x^2 = 8^2 = 64 \]
- Calculate \( F_y^2 \):
\[ F_y^2 = 15^2 = 225 \]

4. **Add the Squares**:
\[ F_x^2 + F_y^2 = 64 + 225 = 289 \]

5. **Take the Square Root**:
\[ R = \sqrt{289} = 17 \, \text{N} \]

6. **Conclusion**:
The resultant force is 17 N.

### Final Answer:
The force is 17 N.

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