momentum physics question

Question

An 80 kg man standing at rest on a smooth, level ice surface throws a 200 g ball horizontally with a speed of 25 m/s, relative to Earth.

(a) With what speed and in what direction does the man move?

(b) If the man throws six such balls every 5.0 s, what is the average force acting on him? 

Answer 1

Hi Alex J.,

You should know by now in your course that total momentum doesn't change. So if the guy throws a 200 g ball * 25 m s^-1 (we assume relative to stationary frame of reference), he must acquire the opposite momentum, in the opposite direction to the one he threw the ball in. Assuming, of course, that he is frictionless, etc.

But (b), you are missing vital information. In what direction(s) does he throw the six balls? Since force is in units of kg m s^-2, one might take the "combined" impulses and divide by the time period (5 s). But which combined impulses? Just the balls', or both of theirs'? You will need to think through what is the role of the force. When it moves through a distance, it expends energy, which appears as kinetic energy. Both the man and the balls have kinetic energy, don't they. So some portion of the force "worked" on each, and must have been exerted.

I'll let you ponder that on your own! It's a nice puzzler.

- Cheers, --Mr. d.