To solve this, we’ll apply the law of conservation of momentum for the first part and use Newton's second law for the second part.

Part 1: Final Speed of the Astronaut

Since no external forces act in space, the momentum of the astronaut and tool system remains conserved.

Given dataTo solve this, we’ll apply the law of conservation of momentum for the first part and use Newton's second law for the second part.

Part 1: Final Speed of the Astronaut

Since no external forces act in space, the momentum of the astronaut and tool system remains conserved.

Given

• Initial speed of astronaut (with tool): $v_i = 0.1 \, \text{m/s}$ (converted from 10 cm/s).
• Mass of astronaut (after releasing tool): $m_a = 180 \, \text{kg}$.
• Mass of tool: $m_t = 20 \, \text{kg}$.
• Speed at which the tool is thrown: $v_t = 10 \, \text{m/s}$.

Since momentum is conserved:

$\text{Initial Momentum} = \text{Final Momentum}$

The initial momentum of the system is: $(m_a + m_t) \times v_i = (180 + 20) \times 0.1 = 200 \times 0.1 = 20 \, \text{kg m/s}$

After the tool is thrown, the total momentum is split between the astronaut and the tool: $m_a \times v_a + m_t \times v_t = 20 \, \text{kg m/s}$

Rearranging to solve for $v_a$, the final speed of the astronaut: $v_a = \frac{20 - m_t \times v_t}{m_a}$ $v_a = \frac{20 - (20 \times 10)}{180} = \frac{20 - 200}{180} = \frac{-180}{180} = -1 \, \text{m/s}$

Thus, the astronaut's final speed is $v_a = 1 \, \text{m/s}$ in the direction opposite to the tool’s throw.

Part 2: Force Exerted by the Astronaut

To find the force exerted, we use the impulse-momentum theorem, which states:

$\text{Force} = \frac{\Delta p}{\Delta t}$

The change in momentum $\Delta p$ for the tool is: $\Delta p = m_t \times v_t - 0 = 20 \times 10 = 200 \, \text{kg m/s}$

Since the time taken for the throw is $\Delta t = 0.5 \, \text{s}$:

$\text{Force} = \frac{200}{0.5} = 400 \, \text{N}$

Summary of Answers:

• Final speed of the astronaut: $1 \, \text{m/s}$ in the opposite direction to the tool's throw.
• Force exerted by the astronaut: $400 \, \text{N}$.

Would you like further clarification on any part?

Related Questions

1. What would happen if the astronaut had a heavier tool?
2. How would the astronaut's speed change if they threw the tool slower?
3. What factors influence the astronaut's ability to maneuver in space?
4. If the astronaut threw two tools in opposite directions, what would be their net speed?
5. How does throwing the tool affect the astronaut’s kinetic energy?

Tip: In space, without external forces, momentum conservation is the key principle for movement.