Atmospheric conditions near a mountain range are such that a cloud at an altitude of 2.00 km contains 3.20 ✕ 10^7 kg of water vapor. How long (in years) would it take for a 2.96 kW pump to raise this amount of water (at a constant speed) from Earth's surface to the altitude of the cloud?

time required is 6.72 years

Explanation:

Given data

mass m = 3.20 ✕ 10^7 kg

height h = 2.00 km = 2 * 10^3 m

power p = 2.96 kW = 2.96 * 10^3 J/s

to find out

time period

solution

we know work is mass * gravity force * height

and power is work / time

so we say that power = mass gravity force * height / time

now put all value and find time period

power = mass * gravity force * height / time

2.96 * 10^3 = 3.20 ✕ 10^7 * 9.81 * 2 * 10^3 / time

time = 62.784 * 10^10 / 2.96 * 10^3

time = 21.21081081 * 10^7 sec

time = 58.91891892 * 10^3 hours

time = 6.72 years

so time required is 6.72 years