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Answer:
His average power is 246.63 Watts
Explanation:
In this problem, we are going to solve for the average power of a marathon runner using the relationship of work, energy, and power. Here, we can solve first the potential energy of the runner which is equivalent to his work and later solve his average power. To do this, we will use the formula
a. PE = mgh
where
PE is the potential energy, the unit is in Joules (J)
m is the mass, the unit is in kg
g is the Earth's pull of gravity, 9.8 m/s²
h in the height, the unit is in meter (m)
b. P = W /t
where
P is the power, the unit is in J/s or Watts
W is the work, the unit is in Joules (J)
t is the time, the unit is in seconds (s)
Given information
m = 50 kg
h = 453 m
t = 15 min = 900 s
P = ?
Solving the problem
First, let us solve for the potential energy which is also equivalent to work
Work = PE
PE = mgh
Then substitute the given data
PE = (50 kg)(9.8 m/s²)(453 m)
PE = 221,970 J
Therefore, Work = 221,970 J
Now, let us solve the average output power of the runner using the given formula
P = W/t
Then substitute the given data
P = 221,970 J / 900 s
P = 246.63 Watts
Therefore, the average power of the runner is 246.63 Watts
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