which change would cause the largest increase in a mountain climbers gravitational potential…

Explanation:

Step1: Recall gravitational - potential - energy formula

The gravitational potential energy formula is $U = mgh$, where $m$ is mass (weight is $W=mg$), $g$ is the acceleration due to gravity, and $h$ is the height.

Step2: Analyze each option

Option 1:

If the original weight is $W = mg$ and height is $h$, the original potential energy is $U_1=mgh$. New weight is $W' = 2mg$ and new height is $h'=\frac{h}{2}$. Then the new potential energy $U'_1=(2mg)\times\frac{h}{2}=mgh$.

Option 2:

New weight is $W'=\frac{mg}{2}$ and new height is $h'=\frac{h}{2}$. Then the new potential energy $U'_2=\frac{mg}{2}\times\frac{h}{2}=\frac{1}{4}mgh$.

Option 3:

New weight is $W' = 2mg$ and new height is $h' = 2h$. Then the new potential energy $U'_3=(2mg)\times(2h)=4mgh$.

Option 4:

New weight is $W'=\frac{mg}{2}$ and new height is $h' = 2h$. Then the new potential energy $U'_4=\frac{mg}{2}\times(2h)=mgh$.

Answer:

carrying twice the weight and climbing twice as high