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)

Question

Responses

21,599,200 J
21,599,200 J

2,204,000 J
2,204,000 J

211,672,160 J
211,672,160 J

10,799,600 J

Answer 1

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

$$PE=m\cdot g\cdot h$$

where:

• $m$ is the mass of the object (in kilograms),
• $g$ is the acceleration due to gravity (approximately $9.81,{\text{m/s}}^2$),
• $h$ is the height above ground (in meters).

Given:

• $m=38,000,\text{kg}$
• $g=9.81,{\text{m/s}}^2$
• $h=58,\text{m}$

Now plug in the values:

$$PE=38,000,\text{kg}\cdot 9.81,{\text{m/s}}^2\cdot 58,\text{m}$$

Calculating it step-by-step:

1. Calculate $g\cdot h$: $$9.81,{\text{m/s}}^2\cdot 58,\text{m}=569.98,{\text{m}}^2/{\text{s}}^2$$

2. Now multiply by the mass $m$: $$PE=38,000,\text{kg}\cdot 569.98,{\text{m}}^2/{\text{s}}^2\approx 21,599,240,\text{J}$$

So the potential energy of the water tank is approximately $21,599,240,\text{J}$, which can be rounded to $21,599,200,\text{J}$.

The correct answer is:

21,599,200 J