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# A large man and a small boy stand facing each other on frictionless ice. They put their hands together and push against each other so that they move apart. Which of the following is true?

(1) The boy moves away with the higher speed
(2) The man moves away with higher speed
(3) Both of them are pushed away with the same speed but different distances
(4) The boy moves farther than the man in the same time interval
(5) They both move the same distance in the same time interval
(6) Both of them are pushed away with the same speed and move same distances apart

(1) The boy moves away with the higher speed:
According to Newton’s third law, the force exerted by the man on the boy and the force exerted by the boy on the man are an action–reaction pair, and so they must be equal in magnitude.
Therefore, the boy, having the smaller mass, experiences the greater acceleration.
Both individuals accelerate for the same amount of time, but the greater acceleration of the boy over this time interval results in his moving away from the interaction with the higher speed.
(4) The boy moves farther than the man in the same time interval
Because the boy has the greater acceleration and, therefore, the greater average velocity, he moves farther during the time interval in which the hands are in contact.
Source: AP Physics textbook Ch5