To tackle this problem, we need to determine the power of a pump that lifts a certain mass of water to a given height within a specified time. Here is the step-by-step solution:
1. Given Data:
- Mass of the water ([tex]\(m\)[/tex]): 200 kg
- Height ([tex]\(h\)[/tex]): 6 meters
- Time ([tex]\(t\)[/tex]): 10 seconds
- Acceleration due to gravity ([tex]\(g\)[/tex]): 9.8 m/s² (this is a standard value)
2. Calculate the Work Done:
- The work done ([tex]\(W\)[/tex]) by the pump in lifting the water can be calculated using the formula for gravitational potential energy:
[tex]\[
W = m \cdot g \cdot h
\][/tex]
- Plugging in the values:
[tex]\[
W = 200 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 6 \, \text{m} = 11760 \, \text{Joules}
\][/tex]
3. Calculate the Power:
- Power ([tex]\(P\)[/tex]) is the rate at which work is done or energy is transferred. It can be calculated using the formula:
[tex]\[
P = \frac{W}{t}
\][/tex]
- Substituting the values:
[tex]\[
P = \frac{11760 \, \text{J}}{10 \, \text{s}} = 1176 \, \text{Watts}
\][/tex]
4. Convert Power to Kilowatts:
- Since 1 kilowatt (kW) = 1000 watts (W), we can convert the power from watts to kilowatts by dividing by 1000:
[tex]\[
P_{\text{kW}} = \frac{1176 \, \text{W}}{1000} = 1.176 \, \text{kW}
\][/tex]
Therefore, the power of the pump is 1.176 kW.
Conclusion:
The given choices for the power are:
a) 12,000 W
b) 1.20 kW
c) 120 W
d) None of the above
Comparing the calculated power of 1.176 kW with the given options, we see that none of the options match exactly, but 1.176 kW is closest to option b) 1.20 kW. So, the best answer, considering the possibilities, is:
b) 1.20 kW since it is the closest to the calculated value of 1.176 kW.
