Answer:
[tex]y\approx 5\ m[/tex]
Explanation:
The pressure of a Fluid
A fluid of density [tex]\rho[/tex] exerts pressure at a distance y (deep) given by
[tex]P=\rho\cdot y\cdot g[/tex]
Where g is the acceleration of gravity or [tex]g=9.8\ m/s^2[/tex]
This formula computes the pressure assuming the initial pressure is 0 at fluid (water in this case) level.
Knowing the measured pressure, we can know how deep the diver went by solving the equation for y
[tex]\displaystyle y=\frac{P}{\rho\cdot g}[/tex]
Let's plug in the given values
[tex]P=50,000\ Pa= 50,000\ N/m^2[/tex]
[tex]\rho=1,000\ kg/m^3[/tex]
[tex]g=9.8\ m/s^2[/tex]
Thus
[tex]\displaystyle y=\frac{50,000\ N/m^2}{1,000\ kg/m^3\cdot 9.8\ m/s^2}[/tex]
[tex]y\approx 5\ m[/tex]
