Final answer:
The power needed for elevator B is four times greater than that for elevator A because elevator B has twice the speed and twice the weight of elevator A.
Step-by-step explanation:
The power needed to lift elevator B, compared to the power needed to lift elevator A, can be determined by considering the relationship between power, weight, and speed. Since power is the rate at which work is done and work is equal to the product of force and distance, lifting a heavier weight (force) over the same height (distance) requires more work. Additionally, lifting at a higher speed means this work is done in a shorter time, thereby requiring more power.
Elevator B moves with twice the speed of elevator A and weighs twice as much. Therefore, the power to lift Elevator B is twice that due to its speed and another twice due to its weight. Multiplying these factors together, the power needed for elevator B is four times greater than that for elevator A.
The correct answer to the question is therefore: A) Four times greater.