Final answer:
The power of the boy can be calculated by first finding the work done as he climbs the staircase, which is his weight times the total height, and then dividing that work by the time taken. With a mass of 50 kg and a staircase height of 6.75 m, the work done is 3303.375 J, and when climbed in 9 seconds, the power is approximately 367 Watts.
Step-by-step explanation:
To calculate the power of the boy when running up the stairs, we can use the formula for power which is the rate of doing work over time (P = W/t). First, we need to calculate the work done, which is equal to the force applied times the distance over which the force is applied. The force here is equivalent to the boy's weight (mass times gravity), and the distance is the total height of the staircase.
The boy's mass (m) is 50 kg and the acceleration due to gravity (g) is 9.81 m/s2. There are 45 steps each with a height (h) of 15 cm, which is 0.15 m per step. Multiplying the number of steps by the height per step gives the total height:
Total height = 45 steps * 0.15 m/step = 6.75 m.
The work done (W) is equal to the boy's weight times the total height:
W = m * g * h = 50 kg * 9.81 m/s2 * 6.75 m = 3303.375 J (Joules).
Now, since he completes this in 9 seconds, the power (P) is:
P = W/t = 3303.375 J / 9 s = 367.042 W (Watts).
Therefore, the power of the boy as he runs up the staircase is approximately 367 Watts.