Problem 8-61 (Alternate Solution) Cons. of Momentum - C

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

Actually any one of the equations could be used, it is only a matter of defining + and - directions. The third equation is probably the most straightforward with + to the right and - to the left

(A)   \(0 = 100m_1 + m_2v'_2\)

(B)   \(0 = 100m_1 - m_2v'_2\)

(C)   \(0 = -100m_1 + m_2v'_2\)

\(0 = -100m_1 + 3.25m_1v'_2\; \text{ or} \\ v'_2  = 30\; m/s\)

but that is relative to the companion ship going at \(350 \;m/s\) so

\(v'_2  = 350 + 30 = 380\; m/s\)

as before.

You have completed this problem.