A uniform chain of length L, measured in 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, air resistance is ignored, and the positive direction is taken to be downward, then

(a) Solve for v in terms of x. Solve for x in terms of t. Express v in terms of t.

(b) Determine how long it takes for the chain to fall completely to the ground.

(c) What velocity does the model in part (a) predict for the upper end of the chain as it hits the ground?

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d?x = Lg. (L - x)- dr dt