A 60 kg skydiver moving at terminal speed falls 50 m in 1 sec. What power is the skydiver expending on the air? The terminal speed of the falling object is the maximum constant speed the object will reach due to the opposing force of air resistance.

To calculate the power expended by the skydiver on the air, we need to know the work done by the skydiver in overcoming air resistance.

The work done can be calculated using the formula:

Work = Force x Distance

The force due to air resistance can be calculated using the formula:

Force = Weight - Drag

Where Weight = mass x acceleration due to gravity, and Drag = 0.5 x density of air x coefficient of drag x velocity² x cross-sectional area.

Given:
Mass of the skydiver (m) = 60 kg
Distance (d) = 50 m
Time (t) = 1 sec
Terminal speed (v) = ?
Density of air (ρ) = assume a standard value of 1.2 kg/m³
Coefficient of drag (C) = assume a standard value of 0.5

First, let's find the terminal speed (v) of the skydiver:

Terminal speed is the maximum constant speed reached when the opposing force of air resistance is equal to the force due to gravity.

Force due to air resistance (Drag) = Weight

0.5 x ρ x C x v² x A = m x g

Here, A denotes the cross-sectional area of the skydiver, which is assumed to be constant.

The weight of the skydiver is given by:

Weight = m x g

m x g = 60 kg x 9.8 m/s²
= 588 N

Now we can solve for the terminal speed (v):

0.5 x ρ x C x v² x A = 588 N

v² = (2 x 588 N) / (0.5 x 1.2 kg/m³ x 0.5 x A)
v² = 1960 / (0.3 x A)
v² ≈ 6533.33 / A

Next, let's calculate the power expended by the skydiver on the air. Power is the rate at which work is done, so we divide work by time:

Power = Work / Time

We can find work by plugging in the values into the work formula:

Work = Force x Distance

Work = (Weight - Drag) x Distance

Now substitute the values to calculate the power:

Power = Work / Time
= [(Weight - Drag) x Distance] / Time

Remember to solve for Drag using the equation:

Drag = 0.5 x ρ x C x v² x A

Finally, substitute the calculated value of Drag and the given values into the formula to find the power expended by the skydiver on the air.

To calculate the power the skydiver is expending on the air, we can use the formula:

Power = Work / Time

First, let's calculate the work done by the skydiver. The work done is equal to the force exerted by the skydiver multiplied by the distance over which the force is applied. In this case, the force is given by gravity, which is the product of the mass and acceleration due to gravity (g). So, the work done is:

Work = Force * Distance

The force is equal to the weight of the skydiver, which is the product of mass and the acceleration due to gravity:

Force = Mass * Acceleration due to gravity

Now, we can calculate the work done:

Work = (Mass * Acceleration due to gravity) * Distance

Given that the mass of the skydiver is 60 kg, the acceleration due to gravity is approximately 9.8 m/s², and the distance fallen is 50 m, we can substitute these values into the equation:

Work = (60 kg * 9.8 m/s²) * 50 m

Next, we need to calculate the time taken. We are given that the skydiver falls 50 m in 1 second. So, the time is:

Time = 1 second

Now, we have all the required values to calculate the power:

Power = Work / Time = [(Mass * Acceleration due to gravity) * Distance] / Time

Substituting in the known values:

Power = [(60 kg * 9.8 m/s²) * 50 m] / 1 second

Now, we can solve for the power:

Power = (5880 kg·m²/s²) / 1 second

Therefore, the power the skydiver is expending on the air is equal to 5880 watts.

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WeighWs = mg = 60kg * 9.8N/kg = 588N. = Weight of skydiver.

P = Fs * V = 588 * 50m/s = 29,400 J/s =
29,400 Watts.