In Space, an astronaut releases a wrench from his hand. The wrench has a mass of 4 grams and is traveling with a velocity of -15m/s. The Astronaut’s mass is 70kg. What is his Velocity?

The velocity of the astronaut is approximately 0.0008571 m/s

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

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