A 60 kg skier leaves the end of a ski-jump ramp with a...

A $60 \mathrm{~kg}$ skier leaves the end of a ski-jump ramp with a velocity of $24 \mathrm{~m} / \mathrm{s}$ directed $25^{\circ}$ above the horizontal. Suppose that as a result of air drag the skier returns to the ground with a speed of 22 $\mathrm{m} / \mathrm{s}$, landing $14 \mathrm{~m}$ vertically below the end of the ramp. From the launch to the return to the ground, by how much is the mechanical energy of the skier-Earth system reduced because of air drag?

Key Concepts

Non-Conservative Forces and Energy Dissipation

Non-conservative forces, such as air drag, do work on a system that dissipates mechanical energy as thermal energy or other forms. This energy loss is calculated by comparing the mechanical energy at different stages of motion and identifying the decrease, which represents the energy transformed by non-conservative work.

Mechanical Energy

Mechanical energy is the sum of kinetic energy and gravitational potential energy in a system. In ideal scenarios without non-conservative forces, mechanical energy is conserved. However, when factors like air drag are present, the total mechanical energy of the system decreases, reflecting energy losses.

Kinetic Energy

Kinetic energy is the energy associated with the motion of an object and is given by the formula (1/2)mv², where m is mass and v is velocity. In problems of projectile motion, the object's speed at launch and upon landing are used to calculate its kinetic energy at those instants, providing insight into how much energy is present in the form of motion.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, typically calculated as mgh where h is the height relative to a reference point. In contexts where an object changes its vertical position, differences in this potential energy become important for analyzing energy transformations.

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