A skydiver of mass 83.7 kg (including outfit and equipment)...

A skydiver of mass $83.7 \mathrm{~kg}$ (including outfit and equipment) falls in the spread-eagle position, having reached terminal speed. Her drag coefficient is $0.587,$ and her surface area that is exposed to the air stream is $1.035 \mathrm{~m}^{2} .$ How long does it take her to fall a vertical distance of $296.7 \mathrm{~m} ?$ (The density of air is $\left.1.14 \mathrm{~kg} / \mathrm{m}^{3} .\right)$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Drag Force

Drag force is the resistance force caused by the motion of an object through a fluid like air. It depends on factors including the fluid density, the object’s speed, its drag coefficient, and the cross-sectional area exposed to the flow. In problems involving free-fall with air resistance, balancing the drag force against the gravitational force allows for the determination of terminal velocity.

Terminal Velocity

Terminal velocity is the constant speed that a falling object eventually reaches when the force due to air resistance (drag) equals the gravitational force. At this point, the net acceleration becomes zero, and the object falls at a steady speed. This concept is vital in dynamics when analyzing objects moving through a fluid medium, such as a skydiver falling through the air.

Uniform Motion in Free Fall

When an object reaches terminal velocity, it is in a state of uniform motion with constant speed. This means that the time taken to cover a certain distance can be calculated using the simple relation time equals distance divided by constant velocity. This principle is used to determine how long it takes an object to fall a given distance under steady conditions.

Transcript

Please give Ace some feedback