What is the velocity of the heavier astronaut after two astronauts push each other apart?

What is the velocity of the heavier astronaut after two astronauts push each other apart?

• A. 4 m/s
• B. 9 m/s
• C. 12 m/s
• D. 16 m/s

Answer: (B)

To determine the velocity of the heavier astronaut after two astronauts push each other apart, we can utilize the principle of conservation of momentum. In a closed system where no external forces act, the total momentum before an event must equal the total momentum after that event. Let's say the two astronauts have masses \( m_1 \) and \( m_2 \) where \( m_2 > m_1 \). When they push away from each other, they exert equal and opposite forces on one another, and as a result, they will move away with velocities that are inversely proportional to their masses. If we denote the velocity of the lighter astronaut (with mass \( m_1 \)) as \( v_1 \) and the velocity of the heavier astronaut (with mass \( m_2 \)) as \( v_2 \), due to the conservation of momentum, we can express this relationship as: \[ m_1 v_1 + m_2 v_2 = 0 \] Rearranging gives us: \[ m_2 v_2 = -m_1 v_1 \] From this equation, we can express \( v_2 \): \[ v_2 = -\frac

To determine the velocity of the heavier astronaut after two astronauts push each other apart, we can utilize the principle of conservation of momentum. In a closed system where no external forces act, the total momentum before an event must equal the total momentum after that event.

Let's say the two astronauts have masses ( m_1 ) and ( m_2 ) where ( m_2 > m_1 ). When they push away from each other, they exert equal and opposite forces on one another, and as a result, they will move away with velocities that are inversely proportional to their masses.

If we denote the velocity of the lighter astronaut (with mass ( m_1 )) as ( v_1 ) and the velocity of the heavier astronaut (with mass ( m_2 )) as ( v_2 ), due to the conservation of momentum, we can express this relationship as:

[

m_1 v_1 + m_2 v_2 = 0

]

Rearranging gives us:

[

m_2 v_2 = -m_1 v_1

]

From this equation, we can express ( v_2 ):

[

v_2 = -\frac