Question

Which change would cause the largest increase in a mountain climber’s gravitational potential energy?

carrying twice the weight and climbing half as high
carrying half the weight and climbing half as high
carrying twice the weight and climbing twice as high
carrying half the weight and climbing twice as high

Answer 1

Gravitational potential energy ΔPE = m g h, so it’s proportional to the product m·h.

Let baseline be m and h. Then:

- 2m, 0.5h → 2·0.5 = 1 × baseline
- 0.5m, 0.5h → 0.5·0.5 = 0.25 × baseline
- 2m, 2h → 2·2 = 4 × baseline
- 0.5m, 2h → 0.5·2 = 1 × baseline

Largest increase: carrying twice the weight and climbing twice as high.