Question

a 63.0 kg astronaut is on a spacewalk when the tether line to the shuttle breaks. The astronaut is able to throw a spare 10.0 kg oxygen tank in a direction away fromthe shuttle with a speed of 12.0 m/s, propelling the astrounaut back to the shuttle. Assuming that the astrounaut starts from rest with respect to the shuttle, findthe astronaut's final speed with respect to the shuttle after the tank is thrown

Answer 1

1. There are other forces at work here however we will pretend it is just a conservation of momentum exercise .
(Also you have one light astronaut)

m1V1=m2V2

V1= (m2/m1)V2
V1= (10/63) 12 = 1.9 m/s

Answer 2

conservation of momentum
(m+M)v = mv_2 + Mv_3
Initially at rest so..
0 = mv_2 +Mv_3
Well call the direction away from the spaceship to be negative
0 = (63 kg * v_2) + (10 kg * -12 m/s)
-v_2 = (10 kg * -12 m/s)/(63kg)
v_2 = 1.9 m/s

Answer 3

Mv¹=Mv² 63×12=10 vf² vf²=63×12÷10 =75.5