5. A ball of mass m gm and radius 7 cm is released from rest in a liquid of viscosity gm/(cm sec). The ball falls under the influence of gravity but the liquid exerts a drag proportional to its velocity v cm/sec. If y cm measures the vertical distance the ball has fallen, then its equation of motion is m d²y dt² dy + 6πμη = mg. dt Determine y(t). What can you say about the velocity v(t)? Suppose a steel ball of density p = 8 gm/cc is dropped in water (μ = 0.01 gm/(cm sec)). Determine the radius of the ball that will fall steadily at 5.05 mph (the fastest speed of a swimmer). Answer: 0.35 mm.

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