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400) In a scene from a movie a cowboy sheriff shoots Bad Jake with a shotgun....

400) In a scene from a movie a cowboy sheriff shoots Bad Jake with a shotgun. This propels the bad guy backwards 2.00 meters/second. The stunt-man playing Bad Jake has a mass of 100kg.
a) Is this an elastic, perfectly inelastic, or only partly elastic collision? What cue(s) told you which?
b) The projectile is stopped in a bullet-proof vest Bad Jake is wearing, resulting in his being thrown back. If the shotgun shoots a 1oz projectile (280.0 grams), what must have been the velocity of the projectile?
c) Does the stunt man playing the bad guy want a thick bullet-proof vest or a thin one? Explain. (You may refer either to the Work-Kinetic Energy theorem, or the Impulse-Momentum one, or find another way.)

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