Question

A diver goes under water and measures the pressure. At some point his instruments read a pressure of 50,000 Pa. How deep did the diver go in meters? The density of water is 1000 kg/m^3. (Write the number only with 1 significant figure)

Answer 1

`y\approx 5\ m`

Step-by-step explanation:

The pressure of a Fluid

A fluid of density
`\rho` exerts pressure at a distance y (deep) given by

`P=\rho\cdot y\cdot g`

Where g is the acceleration of gravity or
`g=9.8\ m/s^2`

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

`\displaystyle y=(P)/(\rho\cdot g)`

Let's plug in the given values

`P=50,000\ Pa= 50,000\ N/m^2`

`\rho=1,000\ kg/m^3`

`g=9.8\ m/s^2`

Thus

`\displaystyle y=(50,000\ N/m^2)/(1,000\ kg/m^3\cdot 9.8\ m/s^2)`

`y\approx 5\ m`