Understanding the Concepts
* Momentum: Momentum is a measure of an object's mass in motion. It's calculated as mass (m) multiplied by velocity (v): p = m * v
* Conservation of Momentum: In a closed system (like space with no external forces), the total momentum before an event is equal to the total momentum after the event.
Setting up the Problem
1. Initial Momentum: The astronaut and rock are initially at rest, so their total initial momentum is 0.
2. Final Momentum: After the throw, the rock has momentum (m_rock * v_rock), and the astronaut has momentum (m_astronaut * v_astronaut).
Applying Conservation of Momentum
* Initial Momentum = Final Momentum
* 0 = (m_rock * v_rock) + (m_astronaut * v_astronaut)
Solving for the Astronaut's Velocity
1. Rearrange the equation:
v_astronaut = - (m_rock * v_rock) / m_astronaut
2. Plug in the values:
v_astronaut = - (5.9 kg * 5.3 m/s) / 81 kg
3. Calculate:
v_astronaut ≈ -0.38 m/s
The Answer
The astronaut moves backward at approximately 0.38 meters per second. The negative sign indicates the astronaut moves in the opposite direction of the thrown rock.
