Question #42442

A block of mass $m = 2 \text{ kg}$ and density $\rho = 8000 \text{ kg/m}^3$ is released from rest on a rough inclined plane of angle $\theta = 37^\circ$. The entire setup is submerged in a large tank containing a viscous fluid of density $\sigma = 2000 \text{ kg/m}^3$. The coefficient of kinetic friction between the block and the plane is $\mu = 0.25$. The fluid exerts a drag force $F_d = k v^2$ on the block, where $k = 0.6 \text{ kg/m}$ and $v$ is the instantaneous velocity. Assuming the fluid is deep enough, what is the terminal velocity of the block? (Take $g = 10 \text{ m/s}^2$, $\sin 37^\circ = 3/5$)