A force is inclined at an angle of `60^(@)` from the horizontal. If the horizontal component of the force is 40N. Calculate the vertical component.

Options

A. f on the odinate and l on the abscissa
B. f on the ordinate and `sqrt(l)` on the abscissa
C. `f^(2)` on the ordinate and l on the abscissa
D. `f^(2)` on the ordinate and `1//l` on the adscissa

Answer

To solve the problem, we need to find the vertical component of a force that is inclined at an angle of 60 degrees from the horizontal, given that the horizontal component of the force is 40 N.

### Step-by-Step Solution:

1. **Identify the Components of the Force**:
- The force can be resolved into two components: the horizontal component (Fh) and the vertical component (Fv).
- We are given that the horizontal component \( F_h = 40 \, \text{N} \).

2. **Use Trigonometric Relationships**:
- The relationship between the vertical and horizontal components of the force can be expressed using the tangent function:
\[ \tan(\theta) = \frac{F_v}{F_h} \]
- Here, \( \theta = 60^\circ \).

3. **Calculate \( \tan(60^\circ) \)**:
- We know that:
\[ \tan(60^\circ) = \sqrt{3} \]

4. **Set Up the Equation**:
- Substitute the known values into the equation:
\[ \tan(60^\circ) = \frac{F_v}{F_h} \implies \sqrt{3} = \frac{F_v}{40} \]

5. **Solve for the Vertical Component \( F_v \)**:
- Rearranging the equation to solve for \( F_v \):
\[ F_v = 40 \cdot \sqrt{3} \]

6. **Calculate the Final Value**:
- Thus, the vertical component of the force is:
\[ F_v = 40\sqrt{3} \, \text{N} \]

### Final Answer:
The vertical component of the force is \( 40\sqrt{3} \, \text{N} \).

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