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

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.