suppose that you drop bbs onto a bull's-eye marked on the floor. according to the uncertainty principle, the bbs do not necessarily fall straight down from the release point to the center of the bull's-eye but are affected by the initial conditions. (a) if the location of the release point is uncertain by an amount ax perpendicular to the vertical direction and the horizontal component of the speed is uncertain by av derive an expression for the minimum spread axof impacts at the bull's-eye if it is located a distance yo below the release point. (b) modify your result in (a) to include the effect on axof uncertainties ay and av, at the release point.