Answer:
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
[tex]m[/tex]The number of 16-cm-high steps are 407 steps.
Given-
Power produced by the athlete [tex]P[/tex] is 746 [tex]w[/tex].
The time taken [tex]t[/tex] is 1 min or 60 sec.
Mass is 70 kg.
Now the equation of the power produced in terms of mass and time taken can be given as,
[tex]P=\dfrac{mgh}{t}[/tex]
Here, [tex]g[/tex] is the gravity force.
Rewrite the equation to solve it further,
[tex]\dfrac{1}{h} =\dfrac{mg}{Pt}[/tex]
[tex]h=\dfrac{Pt}{mg}[/tex]
Put the values of known variables,
[tex]h=\dfrac{746\times 60}{70\times9.8}[/tex]
[tex]h=65.25[/tex]
Height is 65.25 m or 6525 cm.
To find out the number of 16-cm-high steps ([tex]n[/tex]), the height should be divided by the 16.Therefore,
[tex]n=\dfrac{6525}{16}[/tex]
[tex]n=407[/tex]
Hence, the number of 16-cm-high steps are 407 steps.
For more about the power, follow the link given below-
https://brainly.com/question/1618040
