Question

Whyis the following situation impossible?An astronaut, together with the equipment he carries, has a mass of $\mathbf{150}\mathit{k}\mathit{g}$. He is taking a spacewalk outside his spacecraft, which is drifting through space with a constant velocity. The astronaut accidentally pushes against the spacecraft and begins moving away at $\mathbf{20}\mathbf{.}\mathbf{0}\mathbf{}\mathit{m}\mathbf{/}\mathit{s}$, 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 $\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{}\mathit{m}\mathbf{/}\mathit{s}$ relative to himself. After throwing enough equipment, he starts moving back to the spacecraft and is able to grab onto it and climb inside.

Short answer

In order to reverse motion of the astronaut under the given condition, the final mass of the astronaut and the space suit is much lesser, so the given situation is impossible.

Step-by-step solution

Explain the given information

Consider that an astronaut carries the equipment has the mass of $150kg$. taking a walk in space outside the constantly drifting spacecraft. Accidently, the astronaut pushes against the spacecraft and moves away at the speed of$20.0m/s$. To return, he throws the equipment at a maximum speed, since it is bulky and grabs into the spacecraft.

Why is the given situation impossible?

Consider that relative to the spacecraft, the astronaut has a momentum as follows,

$$\begin{gathered} p=\left(150kg\right)\left(20m/s\right) \\ p=3000m/s \end{gathered}$$

He throws away the equipment to reduce his momentum to zero relative to the spacecraft so that the equipment must have the momentum of at least $3000kg·m/s$ .

If the equipment was thrown at the$5.00m/s$relative to himself, then the velocity of the equipment will $25.0m/s$away from the spacecraft.

To equate the momentum, the mass travelling at $25.0m/s$must be equal to $3000kg·m/s$.

$$\begin{gathered} p=3000kg.m/s \\ p=m\left(25.0m/s\right) \end{gathered}$$

Hence,

$$\begin{gathered} m=\frac{3000kg.m/s}{\left(25.0m/s\right)} \\ m=120kg \end{gathered}$$

Therefore, in order to reverse motion of the astronaut under the given condition, the final mass of the astronaut and the space suit is$30kg$ that much lesser, so the given situation is impossible.