During a workout, the football players ran up the stadium stairs in 59 s. The stairs are 140 m long and inclined at an angle of 40°. If a typical player has a mass of 103 kg, estimate the average power output on the way up. Ignore friction and air resistance.
power= work/time= mgh/time h is the verticaldistance moved.
To estimate the average power output of a football player while running up the stadium stairs, we can use the formula:
Power = (Work Done) / (Time)
To calculate the work done, we need to consider the force exerted by the player and the distance traveled.
First, let's find the vertical distance the player climbs along the stairs. We can use trigonometry to find the vertical component of the distance:
Vertical distance = Distance x sin(angle)
Vertical distance = 140 m x sin(40°)
Next, we can calculate the work done. Work is equal to the force applied multiplied by the distance traveled:
Work = Force x Distance
To calculate the force, we need to consider the weight of the player. We can use the formula:
Force = Mass x Gravity
where the mass is given as 103 kg and gravity is approximately 9.8 m/s^2.
Force = 103 kg x 9.8 m/s^2
Now, we can calculate the work done:
Work = Force x Distance
Note that the distance traveled is the vertical distance calculated earlier.
Work = (103 kg x 9.8 m/s^2) x (140 m x sin(40°))
Finally, we can calculate the average power output by dividing the work done by the time taken:
Average Power = Work / Time
Substituting the values we have:
Average Power = [(103 kg x 9.8 m/s^2) x (140 m x sin(40°))] / 59 s
Evaluating this expression will give us the average power output of the football player.