# Newton's Third Law Problem [Checking Solution]

1. Oct 9, 2013

### oMovements

The problem statement, all variables and given/known data
Two hockey players are standing stationary on the ice facing one another. Player A has a mass of 85kg and Player B is 110kg. They shove each other and player A ends up with a velocity of 1.5m/s [W]. Find the final velocity of Player B.

Solution
Fa=Maaa
Fa=(85)(1.5-0/t)

Fb=Mbab
Fb=(110)(1.5-0/t)

Sub Fb into Fa
(110)(Vfb-0/t) = (85)(1.5-0/t)
110Vfb=127.5
Vfb=1.2 m/s [E]

Last edited: Oct 9, 2013
2. Oct 9, 2013

### rock.freak667

Your answer is correct but what you are really doing is a calculation due to conservation of linear momentum

linear momentum = mass x velocity.

so 110*Vfb = 85*1.5

3. Oct 10, 2013

### Andrew Mason

I think you meant Vfb rather than 1.5 here.
What you have written is correct in the result, but you should not, and need not, assume that the acceleration is constant over the entire collision. So it would be more correct to say that:

Fa on b = mbdvb/dt = -Fb on a = -madva/dt

Since $v_a = \int_0^t \frac{dv_a}{dt} dt$ by integrating both sides of the above equation you see that:

mbvb = -mava

which is just conservation of momentum, as rock.freak has pointed out.

AM