Question

A rain cloud contains 4.2 × 10^5 kg of water vapor. How long would it take for a 4000 W pump to raise the same amount of water to the cloud’s altitude, 3.500 km?

Answer 1

it will take 1,000.42 hours to raise the same amount of water.

Step-by-step explanation:

mass of the water to be raised, m = 4.2 x 10⁵ kg

power applied in lifting the water, P = 4000 W

height through which the water will be lifted, h = 3.500 km = 3,500 m

The power applied the water is given as follows;

`Power = Force * Velocity\\\\P = FV\\\\P = ma \ * \ V\\\\P = ma \ * \ (d)/(t) \\\\P = mg \ * \ (h)/(t) \\\\P = (mgh)/(t) \\\\t = (mgh)/(P) \\\\t = (4.2* 10^5 * 9.8 * 3,500)/(4,000) \\\\t = 3,601,500 \ s = 1000.42 \ hours`

Therefore, it will take 1,000.42 hours to raise the same amount of water.