Answer:
The velocity of the astronaut is approximately 0.0008571 m/s
Step-by-step explanation:
The mass of the the wrench, m₁ = 4 grams = 0.004 kg
The velocity of the wrench, v₁ = -15 m/s
The mass of the astronaut, m₂ = 70 kg
The velocity of the astronaut = v₂
Whereby the astronaut and the wrench were initially at rest, we have;
The total initial momentum = 0 kg·m/s
The total final momentum = m₁ × v₁ + m₂ × v₂ = 0.004 kg × (-15 m/s) + 70 kg × v₂
By the conservation of momentum principle, we have;
The total initial momentum = The total final momentum
Therefore, we have;
0 kg·m/s = 0.004 kg × (-15 m/s) + 70 kg × v₂
Which gives;
0.004 kg × (-15 m/s) = 70 kg × v₂
70 kg × -v₂ = 0.004 kg × (-15 m/s)
-v₂ = 0.004 kg × (-15 m/s)/(70 kg) ≈ -0.0008571 m/s
-v₂ ≈ -0.0008571 m/s
v₂ ≈ 0.0008571 m/s
The velocity of the astronaut = v₂ ≈ 0.0008571 m/s