An object $($not necessarily a rectangular prism$)$ is sliding down a ramp inclined at an angle of radians and attains a terminal velocity before reaching the bottom. Assume that the drag force caused by the air is proportional to Sv$2,$ where S is the cross$-$sectional area perpendicular to the direction of motion and v is the speed. Further assume that the sliding friction between the object and the ramp is proportional to the normal weight of the object. Determine the relationship between the terminal velocity and the mass of the object. Using this, if two different boxes $($not necessarily having the same shape$),$ weighing $300$ lb$.$ and $400$ lb$.,$ are pushed down the ramp, find the relationship between their terminal velocities.