How Do Newton's Third Law and Forces Affect Hockey Player Collisions?

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In a collision between a 100 kg and a 112 kg hockey player, both players exert a force of 50N on each other, leading to different accelerations due to their masses. The 100 kg player experiences an acceleration of -1.0 m/s², while the 112 kg player has an acceleration of 0.89 m/s². Newton's Third Law states that forces are equal and opposite, but the resulting accelerations differ because acceleration is inversely proportional to mass. The net force on the system is zero, but the individual forces acting on each player are significant enough to cause movement. Understanding this principle clarifies the confusion regarding the players' motion after the collision.
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So I have a homework question that says:
A 100 kg hockey player a 112kg hockey player collide with each other each traveling with a force of 50N.

The textbook answer says that the acceleration of the 112kg is 0.89m/s^2
and the acceleration of the 100kg player is -1.0 m/s^2.

I'm confused because according to Newton's third Law there will be equal and opposite reaction forces so wouldn't they not move? Is the textbook wrong or am I?
 
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Remember by the second law:

F = m a

They both impart a force of 50N on each other, but the acceleration is also scaled by their masses. 50N on a 100kg person will push them farther than 50N on a 112kg person.


Imagine pushing a shopping cart with 50N. An empty shopping cart will go really far, whereas a full shopping cart will go a much shorter distance. In both instances the force is the same, but:

a = \frac{F}{m}
 
calculating acceleration

So you do 100/100 and 100/112 even though the total of the forces equals 0 because its 50 + -50??
 
The net force of the entire system is 0, but the force on each player is of magnitude 100N. You can find the acceleration of each player using

a = \frac{F}{m}. Knowing F = 100N and m = 100kg for person 1,

a = \frac{100N}{100kg} = 1.0m/s^2

F = 100N and m = 112kg for person 2:

a = \frac{100N}{112kg} = 0.89m/s^2
 
Thank You!

Thank-you you are a saviour!
 
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