Final answer:
The power required by the escalator to carry 50 passengers to a height of 5 meters in 30 seconds, with each passenger averaging 60 kg, is calculated to be approximately 4905 Watts or 4.905 kW. Therefore, the most appropriate answer from the given options is 4.5 kW (Option C).
Step-by-step explanation:
To determine how much power is required by the escalator to carry 50 passengers from the ground floor to the second floor 5 meters above in 30 seconds, we first calculate the work done on the passengers by the escalator. Work is defined as force times distance, where force is the weight of the passengers. The weight can be found by multiplying the total mass of the passengers by the acceleration due to gravity (9.81 m/s²). The total mass can be found by multiplying the average mass of a single passenger by the number of passengers.
Work = Force x Distance = (Total mass) x (Acceleration due to gravity) x (Height)
= (60 kg/passenger x 50 passengers) x 9.81 m/s² x 5 m
= 147,150 Joules
Now, to find the power, which is the rate of work done, we divide the work by the time (30 seconds).
Power = Work / Time = 147,150 J / 30 s = 4905 Watts or 4.905 kW
Therefore, the closest answer to the actual power requirement is Option C, 4.5 kW.