Question

A 116 kg football player is running at 8.05 m/s. A hard-thrown 0.410 kg football has a speed of 23.5 m/s. (Assume the football player is running in the +x-direction.)

Assuming that the football player catches the ball with his feet off the ground with both of them moving horizontally, calculate the following.

(a) the final velocity (in m/s) if the ball and player are going in the same direction (Indicate the direction with the sign of your answer. Enter your answer to at least 3 decimal places.) _______ m/s

(b) the loss of kinetic energy (in J) in this case. ________ J

(c) Repeat parts (a) and (b) for the situation in which the ball and the player are going in opposite directions. (Indicate the direction with the sign of your answer. Enter your answer for the final velocity to at least 3 decimal places.)  final velocity (in m/s) _________ m/s   loss of kinetic energy (in J) ________ J

Might the loss of kinetic energy be related to how much it hurts to catch the pass?

Answer 1

(A) Applying momentum conservation,

(116 x 8.05) + (0.410 x 23.5) = (116 + 0.410) v

v = 8.104 m/s

(B) initial KE , Ki = (116 x 8.05^2)/2 + (0.410 x 23.5^2)/2

Ki = 3871.756 J

final KE , Kf = (116.410) (8.104^2)/2

= 3822.603 J

k_lost = Ki - Kf = 49.153 J

(C) (116 x 8.05) + (0.410 x - 23.5) = (116.410) v

v = 7.939 m/s

(D) Ki = 3871.756 J

Kf = 3668.417 J  

k_lost = 203.338 J  

Yes, lost energy might be related to how much it hurts to catch.