Application Using mass and speed data from Example 8.1 and assuming that the football player catches the ball with his feet off the ground with both of them moving horizontally, calculate: (a) the final velocity if the ball and player are going in the same direction and (b) the loss of kinetic energy in this case. (c) Repeat parts (a) and (b) for the situation in which the ball and the player are going in opposite directions. Might the loss of kinetic energy be related to how much it hurts to catch the pass? Example 8.1 Calculating Momentum: A Football Player and a Football (a) Calculate the momentum of a 110-kg football player running at 8.00 m/s. (b) Compare the player’s momentum with the momentum of a hard-thrown 0.410-kg football that has a speed of 25.0 m/s.
Step-by-step solution In this problem we have to calculate the final velocity of ball and player in the same direction and in opposite direction and also calculate the loss in kinetic energy for same as per the given data respectively: Step 1 of 5 The conservation of momentum for the player and the ball gives, Here, is the mass of player, is the mass of ball, is the initial speed of player and is the initial speed of ball and is the final speed of the ball and player. Step 2 of 5 The final speed of the ball and player is calculated as, Substitute 110 kg for , 0.410 kg for , 8.00 m/s for and 25.0 m/s for . Hence, the final speed of player and ball is . Step 3 of 5 (b) The change in kinetic energy is, Here, is the final kinetic energy of system, is initial kinetic energy of the player and is the initial kinetic energy of ball. Substitute 110 kg for , 0.410 kg for , 8.00 m/s for ,8.06 m/s for and 25.0 m/s for . Hence, the change in kinetic energy is .