A uniform chain of length 8 feet is held vertically so that the lower end just touches the floor. The chain weighs 2 lb/ft. The upper end that is held is released from rest at t = 0 and the chain falls straight down. If x(t) denotes the length of the chain on the floor at time t (in seconds), air resistance is ignored, and the positive direction is taken to be downward, then we have the following. (Take the acceleration of gravity to be 32 ft/s?.) (8 - x) dx dr2 = 256 (a) Let v be the chain's velocityi ft/s. Solve for v in terms of x. Solve for x in terms of t. Express v in terms of t. v(x) = ft/s x(t) = ft v(t) = ft/s (b) Determine how long it takes for the chain to fall completely to the ground. (c) What velocity (in ft/s) does the model in part (a) predict for the upper end of the chain as it hits the ground? O o O va O Lg