Answer to Question #5324 in Mechanics | Relativity for Kyle Mitchell

Question

A rain cloud contains 1.73 × 10^7 kg of water
vapor.The acceleration of gravity is 9.8 m/s^2
.
How long would it take for a 4.9 kW pump
to lift the same amount of water to an altitude
of 24000 m?
Answer in units of years

Answer 1

Let's find the work needed to do that:
A = m*g*H = 1.73*10^7*9.8*24*10^3 = 406.896*10^10 = 406896*10^7 J.
So, the necessary time is:
T = A/P = 406896*10^7 / 4.9*10^3 = 83040*10^4 s = 13840000 minutes = 230666.(6) hours = 9611.(1) days ≈ 26.332 years.