Question

the acceleration due to gravity on the moon is 1.6 m/s². what is the gravitational potential energy of a 1200-kg lander resting on top of a 350-m hill? ~ j
420,000 672,000 1,075,200 4,116,000
how many times more gravitational potential energy would the same lander have on top of a 350-m hill on earth?
it would have dropdown times more gravitational potential energy.

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy (GPE) is \( GPE = mgh \), where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is height.

Step2: Identify the given values for the moon

We have \( m = 1200 \, \text{kg} \), \( g_{\text{moon}} = 1.6 \, \text{m/s}^2 \), and \( h = 350 \, \text{m} \).

Step3: Calculate GPE on the moon

Substitute the values into the formula:
\( GPE_{\text{moon}} = 1200 \times 1.6 \times 350 \)
First, calculate \( 1200 \times 1.6 = 1920 \).
Then, \( 1920 \times 350 = 672000 \, \text{J} \).

Step4: For the Earth comparison (second part, though the first answer is 672000)

On Earth, \( g_{\text{earth}} = 9.8 \, \text{m/s}^2 \). The ratio of \( GPE_{\text{earth}} \) to \( GPE_{\text{moon}} \) is \( \frac{g_{\text{earth}}}{g_{\text{moon}}} = \frac{9.8}{1.6} \approx 6.125 \), but the first question's answer is from the calculation above.

Answer:

For the first question (GPE on the moon), the answer is 672000 J (corresponding to the option 672,000).