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!