A skydiver of mass 80.0 kg jumps from a slow-moving air-...

A skydiver of mass 80.0 kg jumps from a slow-moving air- craft and reaches a terminal speed of 50.0 $\mathrm{m} / \mathrm{s}$ . (a) What is the acceleration of the skydiver when her speed is 30.0 $\mathrm{m} / \mathrm{s}^{2}$ What is the drag force on the skydiver when her speed is (b) 50.0 $\mathrm{m} / \mathrm{s}$ ? (c) When it is 30.0 $\mathrm{m} / \mathrm{s}$ ?

Key Concepts

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F_net = m × a). This principle is used to analyze the motion of objects under various forces, including situations where both gravitational force and drag force are present. It helps in determining the acceleration when the forces are not balanced.

Gravitational Force

Gravitational force is the force exerted by the Earth on a mass, calculated by the formula weight = m × g, where g is the acceleration due to gravity. In free-fall problems, this force is the primary component driving the motion downward, and it serves as a benchmark when comparing with opposing forces like drag.

Terminal Velocity

Terminal velocity is reached when the drag force opposing an object's motion balances the gravitational force, resulting in zero net acceleration. At terminal velocity, the forces in the system are in equilibrium, meaning the object continues to fall at a constant speed. This concept is critical for understanding the dynamics of objects falling through a fluid, such as air.

Drag Force

Drag force is a resistive force exerted by a fluid (like air) on a moving object, and it typically depends on factors such as the object's speed, cross-sectional area, and the properties of the fluid. In many cases, especially at higher speeds, drag force is proportional to the square of the velocity. It plays a key role in determining both the acceleration during free fall (when not at terminal velocity) and the terminal speed of the object.

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