Water falling from a 50 m high fall is to be used for generating electric enegy. If `1.8xx10^5kg` of water falls per hour and half the gravitational potential energyh can be converted into electric energy, how many 100 W lamps can be it?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Convert the mass flow rate from kilograms per hour to kilograms per second.
Given:
- Mass of water falling per hour = \(1.8 \times 10^5 \, \text{kg/h}\)

To convert this to kilograms per second:
\[ \text{Mass flow rate} = \frac{1.8 \times 10^5 \, \text{kg}}{3600 \, \text{s}} = 50 \, \text{kg/s} \]

### Step 2: Calculate the gravitational potential energy per second.
The gravitational potential energy (U) can be calculated using the formula:
\[ U = mgh \]
where:
- \(m\) = mass flow rate (kg/s)
- \(g\) = acceleration due to gravity (approximately \(10 \, \text{m/s}^2\))
- \(h\) = height (50 m)

Substituting the values:
\[ U = 50 \, \text{kg/s} \times 10 \, \text{m/s}^2 \times 50 \, \text{m} = 25000 \, \text{J/s} = 25000 \, \text{W} \]

### Step 3: Calculate the electric energy generated.
Since only half of the gravitational potential energy can be converted into electric energy:
\[ \text{Electric energy} = \frac{1}{2} \times 25000 \, \text{W} = 12500 \, \text{W} \]

### Step 4: Determine how many 100 W lamps can be powered.
To find the number of 100 W lamps that can be powered by the electric energy:
\[ n = \frac{\text{Electric energy}}{\text{Power of one lamp}} = \frac{12500 \, \text{W}}{100 \, \text{W}} = 125 \]

### Final Answer:
The number of 100 W lamps that can be powered is **125**.

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