To determine which student exerted the greatest power, we need to calculate the power exerted by each student. Power is defined as the rate at which work is done, and it can be calculated using the formula:
Power = Work / Time
Since both students lift the boxes to the same height, the work done by each student is equal to the change in potential energy of the box. The change in potential energy can be calculated using the formula:
Change in Potential Energy = mass * gravity * height
Let's calculate the power exerted by each student:
For Student A:
Work = Change in Potential Energy = m * g * h
Power_A = Work / Time
For Student B:
Work = Change in Potential Energy = (2m) * g * (h/2) = m * g * h
Power_B = Work / Time
Since the work done by both students is the same, and the time taken to lift the boxes is assumed to be the same, the power exerted by both students is equal. Therefore, both students exert the same amount of power.