Answer :
Final answer:
To calculate the power produced by the firefighter climbing a ladder, we find the work done (based on the increase in gravitational potential energy) and divide by the time taken. The work done is the product of the firefighter's mass, gravitational acceleration, and the height climbed. Dividing this value by the time yields a power output of approximately 359.6 W, closest to 361 W.
Explanation:
To determine the power generated by the firefighter, we need to calculate the work done by the firefighter climbing the ladder and then divide that by the time it took to do the work. Power is given by the equation:
Power = Work/time
First, we calculate the work done which is equal to the change in gravitational potential energy (as no horizontal distance is involved). Work done by the firefighter can be expressed as:
Work = mass × gravity × height
We know that gravitational acceleration (gravity) on Earth is approximately 9.81 m/s², the firefighter's mass is 105 kg, and the height climbed is 24 m.
Therefore:
Work = 105 kg × 9.81 m/s² × 24 m = 24636.6 joules
Now we will calculate the power. Given that the climb took 68.5 seconds:
Power = 24636.6 joules / 68.5 seconds ≈ 359.6 W
The closest answer to this calculation is 361 W, making this the most likely correct choice from the provided options.
