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Kinetic energy is the energy that an object possesses due to its motion. It's a fundamental concept in physics and is pivotal in understanding how objects move. The formula for kinetic energy is given by \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass of the object and \( v \) is its velocity. This means that the energy is directly proportional to both the mass of the object and the square of its speed.
Since kinetic energy depends on speed, any change in the velocity of an object—such as a water-skier speeding up—results in a change in kinetic energy.
This is exactly what happens when the skier is pulled faster by the boat. His speed increases from 6.10 m/s to 11.3 m/s, leading to an increase in kinetic energy.

• Initial kinetic energy: calculated using the initial speed.
• Final kinetic energy: calculated with the new, higher speed.

Therefore, understanding kinetic energy is crucial for analyzing how the skier's motion changes.

An external force refers to the force applied to an object by something in its environment. In the case of our water-skier, the tow rope connected to the boat is the source of the external force. This force is crucial because it causes the skier to accelerate, changing his speed.
External forces can do work on an object, adding or subtracting energy. In this scenario, the rope pulls the skier, transferring energy from the boat's engine to the skier.
Here's what happens:

• The force pulls the skier at an angle or along a straight path.
• As the skier moves, this force does work, translating energy from the boat to the skier, increasing his speed.

By understanding the external force acting on the skier, we can deduce that positive work is done, increasing his kinetic energy.

Acceleration is the rate at which an object's velocity changes. It can be due to a change in speed or direction. For a water-skier, acceleration happens when the boat increases its throttle, speeding up the skier.
The link between force and acceleration is expressed by Newton's Second Law, \( F = ma \). This law implies that the external force from the tow rope causes the skier's mass to accelerate.
With acceleration, the skier's speed changes over time:

• If acceleration is in the direction of motion, the skier gains speed.
• If it's against the direction, the skier slows down.

Since the skier's speed increased—from 6.10 m/s to 11.3 m/s—it indicates that the acceleration was positive. This ties back to the work-energy principle, as increasing speed leads to more kinetic energy.

Energy change occurs when work is done on or by an object leading to a shift in energy. In our water-skiing scenario, we witness energy change primarily as a change in kinetic energy.
When the external force (tow rope) does work by accelerating the skier, this work correlates directly to an energy change as per the work-energy principle.
This principle states:
The work done on an object equals the change in its energy.

• Initial kinetic energy: when speed was 6.10 m/s.
• Final kinetic energy: when speed rose to 11.3 m/s.

The difference between these kinetic energy values (final - initial) represents the energy change due to work done.
This explanation makes it clear that as the skier was pulled faster, energy was transferred to him, enhancing his motion.