An escalator measures $60\,\text{m}$ in length and raises passengers by a vertical distance of $30\,\text{m}$, as illustrated. When there are no passengers on it, the power needed to drive the escalator against friction is $2.0\,\text{kW}$. The escalator carries passengers with an average mass of $60\,\text{kg}$, while the power needed to overcome friction stays constant. What power is needed to drive the escalator when it is carrying $20$ passengers and moving upwards at $0.75\,\text{m s}^{-1}$?
- A$4.4\,\text{kW}$
- B$6.4\,\text{kW}$
- C$8.8\,\text{kW}$
- D$10.8\,\text{kW}$