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Problem 3.127 - Problem*3.127 Discussion[Difficulty 2...

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Problem *3.127 [Difficulty: 2] Discussion: Separate the problem into two parts: (1) the motion of the ball in water below the pool surface, and (2) the motion of the ball in air above the pool surface. Below the pool water surface the motion of each ball is controlled by buoyancy force and inertia. For small depths of submersion ball speed upon reaching the surface will be small. As depth is increased, ball speed will increase until terminal speed in water is approached. For large depths, the actual depth will be irrelevant because the ball will reach terminal speed before reaching the pool water surface. All three balls are relatively light for their diameters, so terminal speed in water should be reached quickly. The depth of submersion needed to reach terminal speed should be fairly small, perhaps 1 meter or less (The initial water depth required to reach terminal speed may be calculated using the methods of Chapter 9). Buoyancy is proportional to volume and inertia is proportional to mass. The ball with the largest volume per unit mass should
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