four landing sites are proposed for a lander. data about the sites are listed in the table. at which landing…

four landing sites are proposed for a lander. data about the sites are listed in the table. at which landing site would the lander have the greatest amount of gravitational potential energy?\n| landing site | height above surface (m) | acceleration due to gravity (m/s²) |\n| ---- | ---- | ---- |\n| w | 32 | 1.6 |\n| x | 16 | 3.7 |\n| y | 35 | 1.6 |\n| z | 12 | 3.7 |\no w\no x\no y\no z

Answer

Explanation:

Step1: Recall gravitational - potential - energy formula

The formula for gravitational potential energy is $U = mgh$, where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height. Since the mass of the lander is constant, we can compare the products of $gh$ for each site.

Step2: Calculate $gh$ for site W

For site W, $h = 32$ m and $g=1.6$ m/s². So, $gh=1.6\times32 = 51.2$ m²/s².

Step3: Calculate $gh$ for site X

For site X, $h = 16$ m and $g = 3.7$ m/s². So, $gh=3.7\times16=59.2$ m²/s².

Step4: Calculate $gh$ for site Y

For site Y, $h = 35$ m and $g = 1.6$ m/s². So, $gh=1.6\times35 = 56$ m²/s².

Step5: Calculate $gh$ for site Z

For site Z, $h = 12$ m and $g = 3.7$ m/s². So, $gh=3.7\times12 = 44.4$ m²/s².

Step6: Compare the values

Comparing the values of $gh$: $59.2>56>51.2>44.4$. The highest value of $gh$ is for site X.