A 71-kg man can throw a 1-kg ball with a maximum speed of 6 m/s relative to hims

Question

A 71-kg man can throw a 1-kg ball with a maximum speed of 6 m/s relative to himself. Imagine that one day he decides to try to do that on roller skates. Starting from rest, he throws the ball as hard as he can, so it ends up moving at 6 m/s relative to him, but he himself is recoiling as a result of the throw. (a) Assuming conservation of momentum, find the velocities of the man and the ball relative to the ground. (b) What is the kinetic energy of the system right after the throw? (By the system here we mean the man and the ball throughout.) Where did this kinetic energy come from? (c) Is the man's reference frame inertial throughout this process? Why or why not? (d) Is the force exerted by the man on the ball during the throw greater than, equal to, or less than the force exerted by the ball on the man? Why? (e) What is the ratio of acceleration experienced by the man to the acceleration experienced by the ball? (f) Does the center of mass of the system move at all throughout this process?

Explanation / Answer

using conservation of momentum

71 (v) + 1 ( 6) =0 ( where 0 reprsents the initial momentum)

v = 0.084 m/s sec

Velocity of man = - 0.084 m/s , and velocity of ball = 6 m/s with respect to ground

b)KE = 1/2 ( 71) (0.084 )^2 + 1/2 ( 1) (6)^2= 18.25 J apprx

c) No,...because the man is recoiling and ball is moving with respect to earth.

d)As per Newton's 3 law of motopn, both of them exert equal and opposite forces on each other

e)ratio of acceleration = 71 ( 0.084 )/ 1 (6) = 0.994 apprx

f) No

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