Answer to Question #724 in Mechanics | Relativity for Brian

Question

A rain cloud contains 3.36 × 107 kg of water
vapor.
The acceleration of gravity is 9.8 m/s2 .
How long would it take for a 3.6 kW pump
to lift the same amount of water to an altitude
of 17000 m?
Answer in units of years.

Answer 1

The total work of lifting same amount of water is:
A=m*g*h=33,600,000*9.8*17,000=177.5kW*year.
And this work is equal to power*time:
A=W*t => t=A/W=177.5/3.6=49.3 years

Answer 49.3 years