Problem 8-61 Cons. of Momentum - Part 8
A space vehicle and its fuel tank are moving with a velocity of \(350\; m/s\) toward a space station. The fuel tank is then jettisoned to the rear so that its velocity is only \(250\; m/s\) toward the station. What is the new speed of the space vehicle? The mass of the vehicle is \(3.25\) times that of the tank. [Ans. \(380\; m/s\)]
Accumulated Solution
| Solution | Before | After |
|---|---|---|
| (B) | \((m_1 + m_2)v\) | \(m_1\; v_{1}{'} + m_2\; v_{2}{ }'\) |
Correct!
The explosion (or whatever is used) to separate \(m_1\) and \(m_2\) exerts only internal forces on the system.
Therefore momentum is conserved.
\((m_1 + m_2)v = m_1v_1{'} + m_2\; v_2{'}\)
\((m_1 + 3.25\; m_1)(350) = 250\; m_1 + 3.25\; m_1v_2 {'} \\ (4.25)(350) = 250 + 3.25\; v_2{ '} \\ v_2{ '} = [(4.35)(250) – 250]/3.25 = 380 \;m/s\)
You have completed this problem.