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