Final answer:
The child's power output is 78.4 Watts.
To calculate the child's power output, first calculate the work done by multiplying the child's weight by the height climbed, and then divide by the time it took.
Step-by-step explanation:
To calculate the power exerted by a 20 kg child who climbed an 80 cm (0.8 meters) staircase in 2 seconds, you first need to calculate the work done by the child against gravity.
Work is calculated by multiplying force by displacement.
In this case, the force is the weight of the child (mass multiplied by the acceleration due to gravity, which is approximately 9.8 m/s2) and the displacement is the height of the staircase.
The work done (W) can be calculated as:
W = weight × height
W = (20 kg × 9.8 m/s2) × 0.8 m
W = 156.8 Joules
To find the power, which is the rate of doing work, you divide the work done by the time taken. So the power (P) is:
P = Work done / Time taken
P = 156.8 Joules / 2 seconds
P = 78.4 Watts
Therefore, the power output of the child while climbing the stairs is 78.4 Watts.