Serway & Jewett — Linear Momentum and Collisions: Problem 44

Why is the following situation impossible? An astronaut, together with the equipment he carries, has a mass of $150 \text{ kg}$. He is taking a space walk outside his spacecraft, which is drifting through space with a constant velocity. The astronaut accidentally pushes against the spacecraft and begins moving away at $20.0 \text{ m/s}$, relative to the spacecraft, without a tether. To return, he takes equipment off his space suit and throws it in the direction away from the spacecraft. Because of his bulky space suit, he can throw equipment at a maximum speed of $5.00 \text{ m/s}$ relative to himself. After throwing enough equipment, he starts moving back to the spacecraft and is able to grab onto it and climb inside.