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An amoeba of mass 1.0 x 10^-12 kg propels itself through the water by blowing a jet of water through a tiny orifice. Suppose the amoeba ejects water with a speed of 1.0 x 10^-4 m/s and at a rate of 1.0 x 10^-13 kg/s. Assume the water is continuously replenished so the mass of the amoeba stays the same. If there were no force on the amoeba other than the reaction force caused by the emerging jet, what would be the acceleration of the amoeba? If the amoeba moves with constant velocity through the water, what is the force exerted by the surrrounding water (exclusive of the jet) on the amoeba?

A bullet of mass (m) and speed (v) passes copmletely through a pendulum bob of mass (M). The bullet emerges with a speed of v/2. The pendulum bob is suspended by a stiff rod of length l and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical ciricle?