During a baseball game, a batter approaches the plate. The pitcher hurtles the b

Question

During a baseball game, a batter approaches the plate. The pitcher hurtles the ball in the direction of the batter at a speed of 85 miles per hour. The batter swings and makes contact with the ball. The kinetic energy of the ball-batter system is increased by 50%. The ball weighs 5oz. and the batter weighs 195lbs. What is the momentum of the system in the center of mass frame? What is the relative velocity of the system immediately after the collision? What are the velocities of the ball and batter system immediately after the collision?

Explanation / Answer

mass of ball,m1 = 5oz = 0.142 kg mass of batter,m2 = 195 lbs = 88.45 kg speed of ball = 85 mile/hour = 136.8 kmph = 38 m/s initial kinetic energy of system =0.5*mass of ball*speed of ball^2 = 102.524 J since kinetic energy increases by 50% final kinetic energy= 102.524+0.5*102.524 = 153.786 J since during the collision no external force acts on ball and batter system thus momentum remains unchanged momentum = mass of ball*speed of ball = 5.396 kg.m/s

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