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 after throwing the wrench is 8.571 × 10⁻⁴ m/s

Explanation:

The given parameters are;

The mass of the wrench the astronaut releases, m₁ = 4 grams = 0.004 kg

The speed with which the wrench is travelling, v₁ = -15 m/s

The mass of the astronaut, m₂ = 70 kg

The velocity of the astronaut after throwing the wrench = 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 × (-15) + 70 × v₂

By the conservation of momentum principle, we have;

The total initial momentum = The total final momentum

Which gives;

0 = 0.004 × (-15) + 70 × v₂

0.004 × (-15) = -70 × v₂

∴ v₂ = 0.004 × (-15)/-70 = 0.0008571

The velocity of the astronaut after throwing the wrench = v₂ = 0.0008571 m/s = 8.571 × 10⁻⁴ m/s

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