A boy wants to hold a 50 kg box on a snow covered hill. The hill makes an angle of `30^(@)` with the horizontal. What force the boy must exert parallel to the slope ?

Options

A. 25 N
B. 245 N
C. 424 N
D. 490 N

Answer

To solve the problem of determining the force the boy must exert parallel to the slope to hold a 50 kg box on a hill inclined at an angle of 30 degrees, we can follow these steps:

### Step 1: Identify the weight of the box
The weight \( W \) of the box can be calculated using the formula:
\[ W = m \cdot g \]
where:
- \( m = 50 \, \text{kg} \) (mass of the box)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating the weight:
\[ W = 50 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 490 \, \text{N} \]

### Step 2: Resolve the weight into components
The weight of the box can be resolved into two components:
1. **Perpendicular to the slope**: \( W_{\perp} = W \cdot \cos(\theta) \)
2. **Parallel to the slope**: \( W_{\parallel} = W \cdot \sin(\theta) \)

Where \( \theta = 30^\circ \).

Calculating the parallel component:
\[ W_{\parallel} = 490 \, \text{N} \cdot \sin(30^\circ) \]
Since \( \sin(30^\circ) = \frac{1}{2} \):
\[ W_{\parallel} = 490 \, \text{N} \cdot \frac{1}{2} = 245 \, \text{N} \]

### Step 3: Determine the force exerted by the boy
To hold the box stationary on the slope, the boy must exert a force equal to the parallel component of the weight of the box. Therefore, the force \( F \) that the boy must exert is:
\[ F = W_{\parallel} = 245 \, \text{N} \]

### Final Answer
The force the boy must exert parallel to the slope is **245 N**.

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