A 9.40 kg projectile is fired vertically upward. Air drag...

A $9.40 \mathrm{~kg}$ projectile is fired vertically upward. Air drag decreases the mechanical energy of the projectile-Earth system by $68.0 \mathrm{~kJ}$ during the projectile's ascent. How much higher would the projectile have gone were air drag negligible?

Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is calculated based on the height of the object above a reference level and the gravitational acceleration. This concept is crucial in determining how high a projectile will rise once its kinetic energy is entirely converted into potential energy.

Air Drag and Energy Dissipation

Air drag is a non-conservative force that opposes the motion of an object moving through air, resulting in the dissipation of mechanical energy as thermal energy. In projectile motion, the work done against air drag reduces the total mechanical energy available, causing the projectile to reach a lower maximum height than it would in a vacuum.

Energy Conservation

The principle of energy conservation states that energy in an isolated system remains constant over time, though it can change forms. For projectile motion in the absence of non-conservative forces like air drag, the conversion between kinetic and gravitational potential energy is ideal, meaning that all the initial kinetic energy is converted into gravitational potential energy at the peak.

Mechanical Energy

Mechanical energy is the sum of kinetic energy and potential energy in a system. In the context of projectile motion, it encompasses the energy due to the projectile’s motion (kinetic) and its position in a gravitational field (potential). This concept is fundamental when analyzing energy transformations as the projectile ascends and decelerates under gravity.

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