A rain cloud contains 2.72 × 10^7
kg of water vapor.
The acceleration of gravity is 9.81 m/s^2.
How long would it take for a 3.79 kW pump
to raise the same amount of water to the
cloud’s altitude of 1.85 km?
Answer in units of s
To solve this problem, we need to calculate the time it takes for the pump to raise the same amount of water to the cloud's altitude. We can use the work-energy principle to determine the time.
The work done by the pump to raise the water to the cloud's altitude is given by the equation:
Work = mass x gravity x height
In this case, the mass of water to be raised is given as 2.72 × 10^7 kg, the acceleration of gravity is 9.81 m/s^2, and the height is 1.85 km (which needs to be converted to meters).
First, let's convert the height from kilometers to meters:
1.85 km = 1850 meters
Now, we can calculate the work done:
Work = (2.72 × 10^7 kg) x (9.81 m/s^2) x (1850 meters)
Next, we need to calculate the power of the pump, which is given as 3.79 kW. However, we need to convert this to watts since the work-energy equation requires SI units:
Power = 3.79 kW = 3790 watts
Now, we can use the work-energy equation to find the time:
Work = Power x time
Substituting the values we have:
(2.72 × 10^7 kg) x (9.81 m/s^2) x (1850 meters) = 3790 watts x time
Simplifying the equation, we can solve for time:
time = (2.72 × 10^7 kg x 9.81 m/s^2 x 1850 meters) / 3790 watts
Using a calculator, we can compute this value to get the time in seconds.