Final answer:
The thrust on the base of a pool filled with water to a height of 4 meters is calculated using the formula for pressure and the area of the pool's base, resulting in a force of 720 kN, which corresponds to option (a).
Step-by-step explanation:
The question is asking us to estimate the thrust, or force due to pressure, exerted on the base of a rectangular swimming pool when it is filled with water up to a height of 4 meters. This is a basic physics problem that can be solved using the principles of liquid pressure and force.
The pressure exerted by a liquid in an open container due to gravity is given by the formula P = ρgh, where:
P is the pressure
ρ (rho) is the density of the liquid (for water, it's typically 1000 kg/m³)
g is the acceleration due to gravity (approximately 9.81 m/s²)
h is the height of the liquid column
Thus, the pressure at the base of the pool is:
P = 1000 kg/m³ * 9.81 m/s² * 4 m
The force exerted on the base is the pressure multiplied by the area of the base, A. The area of the base is A = length × width, which is 10 m × 18 m. The thrust, or force, is calculated as:
F = P × A
Upon calculating the above, we find that the force (thrust) on the base of the pool is 720 kN, making (a) 720 kN the correct option.