F=ma 2024 Problem 24

Physics · mechanics

Problem

Question: When a projectile falls through a fluid, it experiences a drag force proportional to the product of its cross-sectional area, the fluid density

\rho_{f}

, and the square of its speed. Suppose a sphere of density

\rho_{s} \gg \rho_{f}

of radius

R

is dropped in the fluid from rest. When the projectile has reached half of its terminal velocity, which of the following is its displacement proportional to? (A)

R\sqrt{\rho_{s}/\rho_{f}}

. (B)

R \rho_{s}/\rho_{f}

. (C)

R (\rho_{s}/\rho_{f})^{3/2}

. (D)

R (\rho_{s}/\rho_{f})^2

. (E)

R (\rho_{s}/\rho_{f})^{3}

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