A force acts on a body at a certain angle with the horizontal such that the vertical component is twice the horizontal component . What is the inclination of the force ?

Explanation

To solve the problem of finding the inclination of a force acting on a body such that the vertical component is twice the horizontal component, we can follow these steps:

### Step 1: Define the Components of the Force
Let \( F \) be the magnitude of the force. The force can be resolved into two components:
- Horizontal component (\( F_H \))
- Vertical component (\( F_V \))

According to the problem, we know that:
\[ F_V = 2 F_H \]

### Step 2: Use Trigonometric Relationships
The components of the force can also be expressed in terms of the angle \( \theta \) that the force makes with the horizontal:
- The horizontal component is given by:
\[ F_H = F \cos(\theta) \]
- The vertical component is given by:
\[ F_V = F \sin(\theta) \]

### Step 3: Set Up the Equation
From the relationship given in the problem, we can substitute the expressions for \( F_H \) and \( F_V \):
\[ F \sin(\theta) = 2 F \cos(\theta) \]

### Step 4: Simplify the Equation
We can divide both sides of the equation by \( F \) (assuming \( F \neq 0 \)):
\[ \sin(\theta) = 2 \cos(\theta) \]

### Step 5: Use the Tangent Function
We can rearrange the equation to express it in terms of tangent:
\[ \frac{\sin(\theta)}{\cos(\theta)} = 2 \]
This implies:
\[ \tan(\theta) = 2 \]

### Step 6: Find the Angle
To find \( \theta \), we take the arctangent (inverse tangent) of both sides:
\[ \theta = \tan^{-1}(2) \]

### Step 7: Calculate the Angle
Using a calculator or trigonometric tables, we find:
\[ \theta \approx 63.43^\circ \]

### Final Answer
Thus, the inclination of the force is approximately \( 63.43^\circ \).

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