# Influence of impulse on a conservation of linear momentum problem [closed]

I'm preparing for my physics I final, and I'm having some difficulty with this problem

Two astronauts with their respective masses m1= 110Kg and m2= 85 kg are initially in rest in open space (ignore gravity). Then, the first astronaut pushes the second, with the force F= 120N during the time t= .3 seconds

A)What is the impulse DP produced by the first astronaut?

B) find the respective velocities V1 and V2 (as vectors) of the astronauts after they separated from each other in the frame where astronauts were initially at rest (choose the c axis from the first astronaut toward the second)

C) How much work did the first astronaut produce?

I was able to get A pretty easily, impulse=∆momentum=F∆t=.3*120=36 N*s.

I then ran into trouble. I couldn't use algebra to get a momentum equation going, as I had two unknown variables (V1 and V2), so I used kinematics in one plane, and Newtons second law. F=mass(acceleration), acceleration=F/mass. I substituted this for acceleration into Velocity= Initial velocity+Acceleration(time), to get V1= -.33m/s and V2=.42 m/s.

However, when I plug those values into the conservation of momentum equation, things start to get wonky. If momentum before is zero, because both velocities are zero, then momentum after has to be 36, because in part A the change in momentum was shown to be 36. However, when I multiply the m1 by v1 and m2 by v2, then I get 36 and -36. These add up to zero, which is not 36.

I don't know where I messed up, and I'd really appreciate help with this problem. Additionally, this is my first time using physics stackexchange, so I'm not too familiar with the formatting. I'll get better!

## closed as off-topic by Yashas, Kyle Kanos, ZeroTheHero, Jon Custer, peterhApr 28 '17 at 0:08

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Here impulse on the total system of the 2 astronauts is 0 since no external force acts on the system . The force exerted by astronaut A is an internal force which by Newron's 3rd law of motion has an equal and opposite reaction which acts on astronaut B. Thus total force is 0 for the system. But if you consider each astronaut separately (cosidering the signs as you have done) imuplse is +36 Ns for astronaut A and -36 Ns for astronaut B. Thus both give the same result.

• So my answers were right? – user295095 Apr 27 '17 at 11:25
• Yes your answers are right if you did the calculation properly. I did not check your calculation. I just gave the reasoning. – Suprabha Apr 27 '17 at 12:16
• Always welcome. – Suprabha Apr 27 '17 at 20:22