A rock is released from rest at the surface of the lake,...

A rock is released from rest at the surface of the lake, where the average water temperature is $15^{\circ} \mathrm{C}$. If $C_{D}=0.5,$ determine its speed when it reaches a depth of $600 \mathrm{~mm} .$ The rock can be considered a sphere having a diameter of $50 \mathrm{~mm}$ and a density of $\rho_{r}=2400 \mathrm{~kg} / \mathrm{m}^{3} .$

Key Concepts

Drag Force

Drag force is the resistive force exerted by a fluid against the motion of an object moving through it. It typically depends on factors such as the fluid density, the object's cross-sectional area, the drag coefficient, and the square of the velocity. In problems involving objects moving under gravity in a fluid, drag is critical to determining how the object's speed changes over time.

Terminal Velocity

Terminal velocity is the constant speed that an object eventually reaches when the drag force equals the net gravitational force acting on it. While an object may not always reach terminal velocity over short distances, the concept helps in understanding the long?term behavior of the object moving through a fluid and is fundamental in analyzing motion when drag is significant.

Newton's Second Law in Fluid Dynamics

This principle governs the motion of objects in a fluid by balancing the forces acting on them. For a submerged object, the net force (which accounts for gravity, buoyancy, and drag) produces acceleration. Understanding this balance is crucial for setting up and solving the equations that describe the object's motion in the fluid.

Buoyancy

Buoyancy is the upward force experienced by an object immersed in a fluid, as described by Archimedes’ principle. It equals the weight of the displaced fluid and reduces the effective weight of the object. This concept is essential when determining the net gravitational force acting on a submerged object.

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