the terminal speed of a sky diver is 160 km / h in the spread-eagle position and 310 km / h in

step 1 So here we're basically solving for the air, using equation 616, solving for the area. So the ar

The terminal speed of a sky diver is 160 km / h in the...

the terminal speed of a sky diver is $160 \mathrm{~km} / \mathrm{h}$ in the spread-eagle position and $310 \mathrm{~km} / \mathrm{h}$ in the nosedive position. Assuming that the diver's drag coefficient $C$ does not change from one position to the other, find the ratio of the effective cross-sectional area $A$ in the slower position to that in the faster position.

Key Concepts

Terminal Velocity

Terminal velocity is the constant speed that an object reaches when the force of gravity is balanced by the drag force acting on it. At this point, there is no further acceleration, and the object continues to fall at a steady rate. This concept is crucial in understanding how differing conditions, such as body orientation, affect the speed at which an object like a skydiver falls.

Drag Force

Drag force is the resistive force exerted by a fluid, such as air, on an object moving through it. It is generally proportional to the square of the velocity, the fluid density, the drag coefficient, and the effective cross?sectional area of the object. This principle is central to analyzing how changes in body position affect the skydiver's descent rate.

Effective Cross?Sectional Area

The effective cross?sectional area is the projected area of an object in the direction of motion that interacts with the fluid to produce drag. Changes in body orientation can significantly alter this area, thereby influencing the drag force experienced and, consequently, the terminal velocity. Comparing these areas under different conditions helps in understanding the dynamics of the fall.

Drag Coefficient

The drag coefficient is a dimensionless number that quantifies the drag or resistance of an object in a fluid environment. It encapsulates the effects of the object's shape, surface texture, and flow conditions, and remains constant for a given body configuration under consistent flow conditions. In problems like this, it allows for direct comparison of the effects of changing cross?sectional area while keeping other factors constant.

Transcript

Please give Ace some feedback