A champion athlete can produce one horsepower (746 W) for a short period of time. The number of 16-cm-high steps a 70-kg athlete could ascend in one minute while expending one horsepower is

407 steps

Explanation:

From the question,

P = mgh/t ... Equation 1

Where P = power, m = mass, g = acceleration due to gravity, h = height, t = time.

Make h the subject of the equation

h = Pt/mg ... Equation 2

Given: P = 746 W, t = 1 minute = 60 seconds, m = 70 kg.

Constant: g = 9.8 m/s²

Substitute into equation 2

h = 746 (60) / (70*9.8)

h = 44760/686

h = 65.25 m

h = 6525 cm

number of steps = 6525/16

number of steps = 407 steps