Two swimmers relax close together on air mattresses in a pool. one swimmer's mass is 48 kg,
and the other's mass is 55 kg. if the swimmers push away from each other,
a. their total momentum triples.
b. their momenta are equal but opposite.
c. their total momentum doubles.
d. their total momentum decreases.

B. their momenta are equal but opposite.

Explanation:

For the law of conservation of momentum, the total momentum of an isolated system is conserved.

If we consider the two swimmers as an isolated system, their total momentum is given by:

At the beginning, they are both relaxing, so they are at rest; therefore their total momentum is zero:

p = 0

Later, they push each other. According to Newton's third law of motion, they push each other with the same force (action-reaction pair), so the change in momentum of each swimmer will be equal to that of the other swimmer (in magnitude), according to

where F is the force applied and the duration of the collision.

Since they amount of momentum they gain is the same (in magnitude), but they both started with zero momentum, than this means that their final momenta have same magnitude; and also, they have opposite direction, since they pushed in opposite directions.

So, the correct answer is

B. their momenta are equal but opposite.

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