Calculation of Power:

To calculate the power developed by a man climbing up a vertical stairway, we need to use the formula:

Power = Work done / Time

Work Done:
The work done by the man can be calculated using the formula:

Work done = Force × Distance

Force:
The force exerted by the man can be calculated using the formula:

Force = Mass × Acceleration

Since the man is climbing up at a constant rate, the acceleration can be taken as 0.

Thus, the force exerted by the man is given by:

Force = Mass × Acceleration
= 110 kg × 0
= 0 N

Distance:
The distance covered by the man can be calculated using the formula:

Distance = Velocity × Time

Given that the man is climbing up at a rate of 2 m/s, the distance covered can be calculated as:

Distance = 2 m/s × Time

Time:
The time taken by the man can be calculated using the formula:

Time = Distance / Velocity

Substituting the value of distance in the above equation, we get:

Time = (2 m/s × Time) / 2 m/s
= Time

Therefore, the time taken by the man is equal to the given time, which is 2 seconds.

Calculation of Power:
Now, substituting the values of force, distance, and time in the formula for power, we get:

Power = Work done / Time
= (Force × Distance) / Time
= (0 N × 2 m/s × 2 s) / 2 s
= 0 N × 2 m/s
= 0 W

Explanation:

The power developed by the man climbing up the vertical stairway is calculated to be 0 watts. This means that the man is not exerting any power or doing any work in this situation. Since the force exerted by the man is 0 N, there is no work done against gravity. Therefore, the power developed is 0 watts.