(a) In Example 5.19 (Section 5.3 ), what value of D is required to make vt=42 m / s for the skyd

step 1 Okay, this is question 542, which tells us to refer back to example 518, where we have a skydive

(a) In Example 5.19 (Section 5.3 ), what value of D is...

(a) In Example 5.19 (Section $5.3 ),$ what value of $D$ is required to make $v_{\mathrm{t}}=42 \mathrm{m} / \mathrm{s}$ for the skydiver? (b) If the skydiver's daughter, whose mass is 45 $\mathrm{kg}$ , is falling through the air and has the same $D(0.25 \mathrm{kg} / \mathrm{m})$ as her father, what is the daughter's terminal speed?

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Key Concepts

Terminal Velocity

Terminal velocity is the steady speed achieved by an object when the net force acting on it becomes zero during free fall. At this point, the gravitational force (weight) is exactly balanced by the drag force, meaning there is no further acceleration. This concept is crucial in understanding the dynamics of objects moving through a fluid, such as air.

Drag Force

Drag force is the resistive force exerted by a fluid against the motion of an object. In many cases, especially at higher speeds or in turbulent flow, this force is proportional to the square of the velocity (v²), and it is represented by a drag parameter. This parameter encapsulates factors like the object's cross-sectional area, the drag coefficient, and the density of the fluid.

Force Equilibrium

Force equilibrium in the context of falling objects is reached when the upward drag force equals the downward gravitational force. This balance, where mg = Dv², allows us to solve for terminal velocity and understand how variations in mass or drag parameters affect the steady speed of the falling object.

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