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

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. 

Please see Alternative solution.