A water-skier is being pulled by a tow rope attached to a boat. As the driver pushes the throttle forward, the skier accelerates. A 71.6-kg water-skier has an initial speed of 5.8 m/s. Later, the speed increases to 11.8 m/s. Determine the work done by the net external force acting on the skier.

the work done is the change in kinetic energy.

W = (1/2)(71.6)(11.8^2 - 5.8^2)

Well, well, well! Looks like the water-skier is getting pulled faster and faster! Let's calculate the work done by the net external force on our speedy friend.

Work done is defined as the change in kinetic energy. So, we need to calculate the initial and final kinetic energies and find the difference.

The formula for kinetic energy is: KE = (1/2) * m * v^2, where m is the mass and v is the velocity.

First, let's find the initial kinetic energy:
KE_initial = (1/2) * m * v_initial^2

Substituting the given values:
KE_initial = (1/2) * 71.6 kg * (5.8 m/s)^2

Calculating:
KE_initial = 1/2 * 71.6 kg * 33.64 m^2/s^2
KE_initial = 604.6248 J

Now, let's find the final kinetic energy:
KE_final = (1/2) * m * v_final^2
KE_final = (1/2) * 71.6 kg * (11.8 m/s)^2

Calculating:
KE_final = 1/2 * 71.6 kg * 139.24 m^2/s^2
KE_final = 4991.4944 J

Now, let's find the change in kinetic energy:
ΔKE = KE_final - KE_initial
ΔKE = 4991.4944 J - 604.6248 J
ΔKE = 4396.8696 J

So, the work done by the net external force on the water-skier is approximately 4396.87 Joules.

That's a lot of work for our skier! Looks like they're getting an intense workout out there on the water!

To determine the work done by the net external force acting on the skier, we will use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

The formula for work is:
Work = Force × Distance × cos(θ)

In this case, the net external force acting on the skier is responsible for accelerating the skier. Thus, the work done is equal to the change in kinetic energy of the skier.

The initial kinetic energy (KE₁) of the skier is given by the equation:
KE₁ = (1/2) × mass × (initial velocity)²

Substituting the given values:
KE₁ = (1/2) × 71.6 kg × (5.8 m/s)²

Similarly, the final kinetic energy (KE₂) of the skier is given by:
KE₂ = (1/2) × mass × (final velocity)²

Substituting the given values:
KE₂ = (1/2) × 71.6 kg × (11.8 m/s)²

The change in kinetic energy (ΔKE) is then calculated as:
ΔKE = KE₂ - KE₁

Substituting the respective values into the equation, we can find ΔKE and the work done by the net external force on the skier:

ΔKE = [(1/2) × 71.6 kg × (11.8 m/s)²] - [(1/2) × 71.6 kg × (5.8 m/s)²]

After calculating ΔKE:

Work = ΔKE

To determine the work done, we need to use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.

The formula for work is:

Work = Change in Kinetic Energy

To calculate the change in kinetic energy, we need to find the initial and final kinetic energies of the water-skier.

The formula for kinetic energy is:

Kinetic Energy = (1/2) * mass * velocity^2

Let's calculate the initial and final kinetic energies:

Initial Kinetic Energy:
Mass = 71.6 kg
Velocity = 5.8 m/s

Initial Kinetic Energy = (1/2) * 71.6 kg * (5.8 m/s)^2

Final Kinetic Energy:
Mass = 71.6 kg
Velocity = 11.8 m/s

Final Kinetic Energy = (1/2) * 71.6 kg * (11.8 m/s)^2

Now, we can calculate the change in kinetic energy by subtracting the initial kinetic energy from the final kinetic energy:

Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy

Finally, we can calculate the work done by substituting the change in kinetic energy into the work formula:

Work = Change in Kinetic Energy

Now, you can plug in the values and solve for Work.