An engine develops 10 kW of power. How much time will it take to lift a mass of 200 kg to a height of 40 m (`g=10(m)/(sec^2)`)`?

Options

A. 4 s
B. 5 s
C. 8 s
D. 10 s

Explanation

To solve the problem, we need to determine how much time it will take for an engine that develops 10 kW of power to lift a mass of 200 kg to a height of 40 m. We will use the concepts of work, energy, and power.

### Step-by-Step Solution:

1. **Identify the given values:**
- Power (P) = 10 kW = 10,000 W (since 1 kW = 1000 W)
- Mass (m) = 200 kg
- Height (h) = 40 m
- Gravitational acceleration (g) = 10 m/s²

2. **Calculate the work done (W):**
The work done in lifting the mass can be calculated using the formula for gravitational potential energy:
\[ W = mgh \]
Substituting the known values:
\[ W = 200 \, \text{kg} \times 10 \, \text{m/s}^2 \times 40 \, \text{m} \]
\[ W = 200 \times 10 \times 40 = 80,000 \, \text{J} \]

3. **Use the power formula to find time (t):**
Power is defined as work done per unit time:
\[ P = \frac{W}{t} \]
Rearranging this formula to solve for time gives:
\[ t = \frac{W}{P} \]
Substituting the values we calculated:
\[ t = \frac{80,000 \, \text{J}}{10,000 \, \text{W}} \]
\[ t = 8 \, \text{s} \]

4. **Conclusion:**
The time taken to lift the mass is 8 seconds.

### Final Answer:
The time taken to lift the mass is **8 seconds**.

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