During a workout, the football players at Rutgers State University ran up the stadium stairs at a steady pace in 48 s. The stairs are 135 m long and inclined at an angle of 35 degree. If a typical player has a mass of 120 kg, estimate the average power output on the way up. Ignore friction and air resistance.(g = 9.8 m/s^2)

To estimate the average power output of a football player running up the stadium stairs, we can use the work-energy principle.

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the player is to overcome the force of gravity while running up the inclined stairs.

First, we need to calculate the total work done by the player. The work done against gravity can be given by the formula:

Work = Force x Distance x cos(theta)

Where:
- Force is the component of the force of gravity acting parallel to the displacement (mg*sin(theta))
- Distance is the length of the stairs (135 m)
- theta is the angle of inclination (35 degrees)

The force of gravity on the player can be calculated using the formula:

Force = mass x acceleration due to gravity (mg)

Where:
- mass is the mass of the player (120 kg)
- acceleration due to gravity (g) is given as 9.8 m/s^2

Now, we can substitute the values into the formulas to calculate the work done against gravity:

Force = mass x g = 120 kg x 9.8 m/s^2 = 1176 N
Work = Force x Distance x cos(theta) = 1176 N x 135 m x cos(35 degrees)

Next, we need to calculate the time taken by the player to complete the workout. We are given that the time taken is 48 s.

Finally, we can calculate the average power output using the formula:

Power = Work / Time

Substituting the calculated values:

Power = (1176 N x 135 m x cos(35 degrees)) / 48 s

Now, we can use a calculator to find the numerical value for the average power output.