Question

A certain rain cloud at an altitude of 1.66 km contains 3.20 ✕ 107 kg of water vapor. How long would it take for a 2.39-kW pump to raise the amount of water from Earth's surface to the cloud's position?

Answer 1

let us consider the potential energy that is contained in the mass of water by using the equation for gravitational potential energy...

G.P.E = Mass * height * acceleration. due to gravity.

E = 3.2 * 10^7 * 1.66 * 1000 * 9.8  

=5.205* * 10^11 Joules

now let us consider the equation of power

Power = Work done / time taken (where work done is the energy required to raise water to such heights, that is "it's GPE")

2.39 1000 = 5.205* * 10^11/T

T = 5.205 * 10^11/2700

So, time taken 'T' = 1.92 x 10^8 secs .