Question

A satellite traveling 800 m/s approaches a second satellite that is at rest. They both have the same mass. What will happen to their speeds when they connect and move off together?

Answer 1

`\bullet~\text{Mass of each satellite:}~m\\\\ \bullet~\text{Linear momentum of the first satellite:}\\p_1=m_1v_1=m\cdot800\Longrightarrow p_1=800m\\\\ \bullet~\text{Linear momentum of the second satellite:}~\\p_2=m_2v_2=m\cdot0\Longrightarrow p_2=0~kg\cdot m/s\\\\ \bullet~\text{Linear momentum of the connected satellites:}~\\p'=m'v'=(m_1+m_2)\cdot v'=(m+m)\cdot v'\Longrightarrow p'=2mv'\\\\`

By the conservation the linear momentum:


`p_(initial)=p_(final)\\\\ p_1+p_2=p'\\\\ 800m+0=2mv'\\\\\ 2mv'=800m\\\\ v'=(800m)/(2m)\\\\ \boxed{v'=400~m/s}`

The speed of the connected satellites is 400 m/s.