From a barrel with a height of 1.5 m and a volume of 6000 liters, the first half is scooped out by a girl

From a barrel with a height of 1.5 m and a volume of 6000 liters, the first half is scooped out by a girl in 5 minutes, and the second by a boy in 6 minutes. how much power does each one develop?

Given:

h = 1.5 meters – barrel height;

V = 6000 liters = 6 m3 – barrel volume;

t1 = 5 minutes = 300 seconds – the time it takes for the girl to scoop out the first half of the barrel;

t2 = 6 minutes = 360 seconds – the time it takes for the boy to scoop out the second half of the barrel;

ro = 1000 kg / m3 – water density.

It is required to determine the power of the girl N1 (Watt) and the boy N2 (Watt).

According to the problem, the girl scoops out the first half of the barrel. That is, it raises half of the water in the barrel to a height equal to h / 2. The perfect work in this case will be equal to:

A1 = F * h / 2 = m * g * h / 2 = ro * V * g * h / 4 = 1000 * 6 * 10 * 1.5 / 4 = 250 * 6 * 10 * 1.5 = 22500 Joules …

Then the power developed by the girl will be equal to:

N1 = A1 / t1 = 22500/300 = 75 watts.

The boy scoops out the other half of the barrel. That is, it raises half of the water in the barrel to a height equal to h. The perfect work will be equal to:

A2 = F * h = m * g * h = ro * V * g * h / 2 = 1000 * 6 * 10 * 1.5 / 2 = 500 * 6 * 10 * 1.5 = 45000 Joules.

Then the boy’s cardinality will be:

N2 = A2 / t2 = 45000/360 = 125 watts.

Answer: the girl’s power is 75 watts, the boy’s is 125 watts.