Question

A rain cloud contains 2.66 × 107 kg of water vapor. How many days would it take for a 3.00 kW pump to raise the same amount of water to the cloud’s altitude, 2.00 km, at a constant speed?

Answer 1

• 2052 days

Step-by-step explanation:

To find the time taken , we can use;

→ Power = work done/time taken

Work done for raising a mass "m" by height "h" is given as;

→ Work done = mgh

Here we have;

• m = 2.66 * 10⁷ kg.
• h = 2km = 2000m.
• g = 9.8 m/s².
• power of pump = 3kW = 3000W.

So we have;

→ P = W/t

→ P = mgh/t

On substituting the respective values, we have;

→ 3000W = 2.66 * 10⁷kg * 10m/s² * 2000m/t

→ t = 2.66 * 10⁸/ 3000 s

Convert it into hours by dividing it by 60*60

→ t = 2.66 * 2 * 10¹¹ / 3000 * 60 * 60 hr

→ t = 49259 hr

Finally convert it into days by dividing it by 24.

→ t = 49259/24 days

→ t = 2052 days

Henceforth it will take 2052 days to do the required work.