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)
• 21,599,200 J
• 211,672,160 J
• 2,204,000 J
• 10,799,600 J

Answer 1

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

\[
PE = mgh
\]

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

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

Now, substituting the values into the formula:

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

Calculating this step-by-step:

1. Calculate \( g \times h \):

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

2. Now, calculate \( m \times (g \times h) \):

\[
PE = 38,000 \, \text{kg} \times 569.98 \, \text{m}^2/\text{s}^2
\]

\[
PE = 21,599,240 \, \text{J}
\]

Rounded to three significant figures, this is approximately:

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

Thus, the potential energy of the water tank is approximately \( \boxed{21,599,200 \, J} \).