Certainly! Let's go step-by-step to calculate the acceleration due to gravity given the depth of water, the pressure at the bottom of the pond, and the density of water.
### Given Data:
- Depth of water ([tex]\(h\)[/tex]): 5 meters
- Pressure at the bottom of the pond ([tex]\(P\)[/tex]): 49,000 Pascals (Pa)
- Density of water ([tex]\(\rho\)[/tex]): 1000 kilograms per cubic meter (kg/m[tex]\(^3\)[/tex])
### Formula to use:
The pressure exerted by a fluid column of height [tex]\(h\)[/tex] and density [tex]\(\rho\)[/tex] is given by:
[tex]\[ P = \rho g h \][/tex]
where:
- [tex]\(P\)[/tex] is the pressure,
- [tex]\(\rho\)[/tex] is the density,
- [tex]\(g\)[/tex] is the acceleration due to gravity,
- [tex]\(h\)[/tex] is the height (depth in this case).
We need to solve for [tex]\(g\)[/tex]:
[tex]\[ g = \frac{P}{\rho h} \][/tex]
### Steps to Solve:
1. Substitute the given values into the formula:
[tex]\[ P = 49,000 \, \text{Pa} \][/tex]
[tex]\[ \rho = 1000 \, \text{kg/m}^3 \][/tex]
[tex]\[ h = 5 \, \text{meters} \][/tex]
2. Calculate [tex]\(g\)[/tex]:
[tex]\[ g = \frac{49,000}{1000 \times 5} \][/tex]
3. Perform the multiplication in the denominator:
[tex]\[ \rho h = 1000 \times 5 = 5000 \][/tex]
4. Now divide the pressure by this product:
[tex]\[ g = \frac{49,000}{5000} \][/tex]
5. Simplify the division:
[tex]\[ g = 9.8 \, \text{m/s}^2 \][/tex]
### Conclusion:
The acceleration due to gravity at the given location, based on the provided data, is approximately:
[tex]\[ g = 9.8 \, \text{m/s}^2 \][/tex]
Thus, we have calculated the acceleration due to gravity as 9.8 meters per second squared.
