Power Depends on Speed, Potential Energy on Height

Steps:

• Gravitational potential energy gained equals mgh, where h is the stair height, same for both methods.
• Mass m and g are constant, so ΔPE is identical regardless of running or walking.
• Power P equals work (ΔPE) divided by time Δt.
• Running reduces Δt compared to walking, increasing P while ΔPE stays the same.

Why C is correct:

• ΔPE = mgh is independent of speed; P = ΔPE/Δt increases with shorter Δt for running.

Why the others are wrong:

• A: ΔPE is the same, not more for running.
• B: ΔPE is the same, and power is more, not the same.
• D: Power is more for running, not the same.

Final answer: C