To solve the problem step by step, we will follow the outlined procedure:
### Step 1: Calculate the energy required for climbing
The energy required to climb to a height \( h \) can be calculated using the formula:
\[
E = mgh
\]
where:
- \( m \) = mass of the man = 80 kg
- \( g \) = acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \))
- \( h \) = height climbed = 200 m
Substituting the values:
\[
E = 80 \, \text{kg} \times 10 \, \text{m/s}^2 \times 200 \, \text{m} = 160000 \, \text{J} = 160 \, \text{kJ}
\]
### Step 2: Determine the energy available from the food intake
The man consumes 20 g of food. We need to calculate the total energy provided by this food. The energy from food can be calculated using the enthalpy of combustion of the food item.
We will check each food option provided in the question.
### Step 3: Calculate the energy from each food option
1. **Wheat Bread**:
- Enthalpy of combustion = 20 kJ/g
- Energy from 20 g = \( 20 \, \text{kJ/g} \times 20 \, \text{g} = 400 \, \text{kJ} \)
2. **Fructose Syrup**:
- Enthalpy of combustion = 13 kJ/g
- Energy from 20 g = \( 13 \, \text{kJ/g} \times 20 \, \text{g} = 260 \, \text{kJ} \)
3. **Olive Oil**:
- Enthalpy of combustion = 35 kJ/g
- Energy from 20 g = \( 35 \, \text{kJ/g} \times 20 \, \text{g} = 700 \, \text{kJ} \)
4. **Fuel Intake** (not specified in the question but can be inferred):
- Enthalpy of combustion = 16 kJ/g
- Energy from 20 g = \( 16 \, \text{kJ/g} \times 20 \, \text{g} = 320 \, \text{kJ} \)
### Step 4: Calculate the useful energy after accounting for waste
Since 60% of the energy is wasted, only 40% is used for climbing work.
- For **Wheat Bread**:
\[
\text{Useful energy} = 0.40 \times 400 \, \text{kJ} = 160 \, \text{kJ}
\]
- For **Fructose Syrup**:
\[
\text{Useful energy} = 0.40 \times 260 \, \text{kJ} = 104 \, \text{kJ}
\]
- For **Olive Oil**:
\[
\text{Useful energy} = 0.40 \times 700 \, \text{kJ} = 280 \, \text{kJ}
\]
- For **Fuel Intake**:
\[
\text{Useful energy} = 0.40 \times 320 \, \text{kJ} = 128 \, \text{kJ}
\]
### Step 5: Compare the useful energy with the required energy
The required energy for climbing is 160 kJ.
- **Wheat Bread** provides exactly 160 kJ of useful energy.
- **Fructose Syrup** provides 104 kJ (not sufficient).
- **Olive Oil** provides 280 kJ (excess).
- **Fuel Intake** provides 128 kJ (not sufficient).
### Conclusion
The only food option that provides enough energy for the climbing work, after accounting for the energy wasted, is **Wheat Bread**.
