A student, late for class, ran up some stairs

between landings. The landings are 8.2 m
apart. The student has a mass of 54.1 kg and
it took 7 s to do the run.
The acceleration of gravity is 9.8 m/s
2
.
What is the average power that the student
was generating during the run?

Well, let's calculate it step by step! First, let's find out the total distance the student traveled. Since the landings are 8.2 m apart, let's assume the student ran up N number of stairs. So, the total distance would be N * 8.2 m. But we don't know N, do we? Maybe N is the neighbor's cat's favorite number or something. So let's stick with N for now.

Next, let's find the average speed of the student. We know that the total distance is N * 8.2 m and it took 7 seconds to complete the run. Therefore, the average speed would be (N * 8.2 m) / 7 s.

Now here comes the tricky part. We need to calculate the work done by the student against gravity. The work done against gravity is equal to the change in potential energy, which is given by m * g * h, where m is the mass of the student, g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical height climbed.

Since we don't know the exact height of each step, let's assume an average height of h meters per step. So, the total height climbed would be N * h meters. The work done against gravity would then be m * g * (N * h).

Now, average power is equal to work done divided by time taken. So, average power = (m * g * (N * h)) / 7 s.

Are you still with me? I know, it's a lot of steps. But hey, we're talking about a staircase, so it's only fitting, right?

Oh, wait! You asked for the average power, not the average power per step. Silly me! Let's divide the above equation by N, so it becomes (m * g * h) / 7 s. Voila! That's the average power generated by the student during the run.

But hey, while we're on the topic of power, did you hear about the mathematician who went to the bakery to buy a pie? He always calculated the circumference of the pie before biting into it. Talk about a sweet tooth for mathematics!

Anyway, back to the question at hand. The average power generated by the student during the run is (m * g * h) / 7 s.

To find the average power generated by the student during the run, we need to use the formula:

Power = Work / Time

The work done by the student can be calculated using the formula:

Work = Force × Distance

First, let's find the force exerted by the student. The force can be calculated using Newton's second law of motion:

Force = Mass × Acceleration

The acceleration can be found using the formula:

Acceleration = Δv / Δt

Here, Δv represents the change in velocity and can be calculated using the formula:

Δv = Final velocity - Initial velocity

Since the student is running up the stairs, the initial velocity is 0 m/s, and the final velocity can be calculated using the formula:

Final velocity = Distance / Time

Substituting the given values into the formulas, we have:

Final velocity = 8.2 m / 7 s

Now, let's calculate the change in velocity:

Δv = Final velocity - Initial velocity
= Final velocity - 0 m/s
= Final velocity

Next, we can calculate the acceleration:

Acceleration = Δv / Δt
= Final velocity / time
= (8.2 m / 7 s) / 7 s

Now, we can find the force exerted by the student using the formula:

Force = Mass × Acceleration
= 54.1 kg × [(8.2 m / 7 s) / 7 s]

Finally, we can calculate the work done by the student:

Work = Force × Distance
= (54.1 kg × [(8.2 m / 7 s) / 7 s]) × 8.2 m

Now, we can substitute the work and time values into the power formula:

Power = Work / Time
= [(54.1 kg × [(8.2 m / 7 s) / 7 s]) × 8.2 m] / 7 s

By calculating the above expression, we can find the average power generated by the student during the run.

To find the average power generated by the student during the run, we need to use the formula:

Average Power = Work / Time

The work done by the student is equal to the change in potential energy. Since the student ran up the stairs, the work done against gravity is equivalent to the increase in potential energy.

The change in potential energy can be calculated using the formula:

Change in Potential Energy = Mass x Gravity x Height

Here, the height represents the vertical distance between the two landings, which is 8.2 m.

So, the change in potential energy can be calculated as:

Change in Potential Energy = Mass x Gravity x Height
Change in Potential Energy = 54.1 kg x 9.8 m/s^2 x 8.2 m

Now, we have the work done by the student, and we can substitute this value along with the given time of 7 s into the formula for average power:

Average Power = Work / Time
Average Power = (54.1 kg x 9.8 m/s^2 x 8.2 m) / 7 s

Now, we can calculate the average power by solving this equation.

P = M g H/t

H = 8.2 m
g = 8.81 m/s^2
t = 7.0 s
M = 54.2 kg

The answer will be in watts.