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

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

We now know that the above drawing is the correct one.
Momentum has to be observed from any frame of reference: We have solved the problem with the observer in the "Lab" frame of reference watching the Ship and its Tank go by.

What about those riding in another ship travelling at \(350\; m/s\) along side? For them the ship and tank are initially at rest so that they see \(v = 0\) as shown in the second drawing. After the separation the tank is moving to the left at \(350-250 = 100\; m/s\) and the ship is moving to the right. Momentum is conserved so:

(A)   \(0 = 100m_1 + m_2v'_2\)

(B)   \(0 = 100m_1 - m_2v'_2\)

(C)   \(0 = -100m_1 + m_2v'_2\)