To calculate the work required to pump the water out of the pool, we need to determine the volume of water in the pool and then multiply it by the product of the density of water and the acceleration due to gravity.
First, let's calculate the cross-sectional area of the pool's base (Aly):
Aly = length x width = 22 m x 11 m = 242 m²
The volume of water in the pool can be found by multiplying the cross-sectional area (Aly) by the uniform depth (2.4 m):
Volume = Aly x depth = 242 m² x 2.4 m = 580.8 m³
Next, we can calculate the mass of water in the pool by multiplying the volume by the density of water:
Mass = Volume x density = 580.8 m³ x 1000 kg/m³ = 580,800 kg
Finally, we can calculate the work (W) required to pump the water out of the pool using the formula:
Work = force x distance
In this case, the force is equal to the weight of the water, which can be calculated using the mass and the acceleration due to gravity:
Force = Mass x gravity = 580,800 kg x 9.8 m/s² = 5,691,840 N (Newtons)
The distance in this case is the height of the pool, which is 2.4 m.
Work = Force x distance = 5,691,840 N x 2.4 m = 13,660,736 J (Joules)
Therefore, the work required to pump the water out of the pool when it is full is approximately 13,660,736 Joules.