An escalator has a length of $60\,\text{m}$ and raises passengers by a vertical distance of $30\,\text{m}$, as illustrated. When no passengers are on it, the power needed to operate the escalator against friction is $2.0\,\text{kW}$. Passengers of mean mass $60\,\text{kg}$ use the escalator, and the power needed to overcome friction stays unchanged. What power is needed to run the escalator while it is carrying $20$ passengers and moving at $0.75\,\text{m s}^{-1}$?
- A$4.4\,\text{kW}$
- B$6.4\,\text{kW}$
- C$8.8\,\text{kW}$
- D$10.8\,\text{kW}$