A61kg astronaut (including spacesuit and equipment), is floating at rest a distance of 10 m from the spaceship when she runs out of oxygen and fuel to power her back to the spaceship. she removes her oxygen tank (3.0 kg) and flings it away from the ship at a speed of 15 m/s relative to the ship. part a: at what speed relative to the ship does she recoil toward the spaceship? my attempt: m1v1=m2v2(3kg)(15m/s) = (61kg)(v2)45 kg*m/s = (61kg)(v2)v2 = .7377 m/s

 v₂ = - 0.776 m / s

Explanation:

We can solve the exercise with the moment. The system is formed by the astronaut plus the oxygen backpack, in this system the forces are internal and the moment is conserved.

Initial moment, before throwing the tank

    p₀ = 0

Final after throwing the tanks

    pf = m₁ v₁ + m₂ v₂

Where m₁ is the mass of the tanks (m₁ = 3.0 kg) and velocity (v₁ = 15 m / s), m₂ is the astronaut's remaining mass, its total mass minus the mass it throws

    m₂ = 61 –m₁

    m₂ = 61 -3

    m₂ = 58 kg

    p₀ = pf

     0 = m₁  v₁ + m₂ v₂

    v₂ = - v₁ m₁ / m₂

    v₂ = -15 3/58

    v₂ = - 0.776 m / s

The negative sign means that the astronaut goes in the opposite direction from where the tank is thrown

your answer is, orbit around the nucleus