1. (25 pts) A small particle is moving through the air at velocity v as sketched to the right. At the location of the particle, and at a given instant in time, the air velocity is U~ as also sketched. (a) Carefully analyze and draw the direction of the aerodynamic drag force on the particle at this instant in time. [The magnitude is arbitrary - the direction is what is important.] (b) Now suppose that the gravitational force on the particle (weight minus buoyancy force) in the downward direction is half the magnitude of the drag force. To scale, acceleration of the particle at this instant in time. [In the end, all we really care abo vector - the magnitude is arbitrary, but make sure that the gravitational force is hal drag force.]