Question

The roof of an apartment building is 58 meters high. A water tank on the roof has a mass of 38,000 kilograms. What is the potential energy of the water tank?(1 point) Responses 211,672,160 J 211,672,160 J 21,599,200 J 21,599,200 J 10,799,600 J 10,799,600 J 2,204,000 J

Answer 1

To find the potential energy (PE) of the water tank, you can use the formula for gravitational potential energy:

\[
PE = mgh
\]

where:
- \( m \) = mass of the water tank (in kilograms)
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))
- \( h \) = height above the ground (in meters)

Given:
- \( m = 38,000 \, \text{kg} \)
- \( h = 58 \, \text{m} \)
- \( g \approx 9.81 \, \text{m/s}^2 \)

Now substituting these values into the formula:

\[
PE = 38,000 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 58 \, \text{m}
\]

Calculating step by step:

1. Calculate \( 9.81 \times 58 \):

\[
9.81 \times 58 \approx 569.98 \, \text{m}^2/\text{s}^2
\]

2. Now multiply this result by the mass:

\[
PE \approx 38,000 \, \text{kg} \times 569.98 \, \text{m}^2/\text{s}^2 \approx 21,599,240 \, \text{J}
\]

Rounding gives:

\[
PE \approx 21,599,200 \, \text{J}
\]

Thus, the potential energy of the water tank is approximately **21,599,200 J**. The correct response from the options given is:

**21,599,200 J**.