1. Using velocity profiles. A gravity driven dust collector is shown below. We wish to determine the minimum length needed that will allow the particle with mass m to reach the bottom before it is swept out of the channel. Assume the flow is laminar and assume that the velocity of the particle in the x direction is the same as the fluid velocity in the x-direction. Assume that drag on the particle can be neglected. a) Solve a force balance (F=ma) in the vertical y direction to obtain the time it takes for the particle to fall to the bottom of the plate. b) Solve for the minimum length, Lmin, considering the horizontal motion. You can use the velocity distribution derived in class. Hint: Remember the definition of the velocity. c) What would happen conceptually to your answer for b) if you were to think about adding particle drag