# Not sure where to start(momentum problem, I think)

by DLxX
Tags: startmomentum
 P: 183 Not sure where to start(momentum problem, I think) Lets divide the problem in two parts: initial and final. INITIAL: "Two children are standing on a 150kg wagon which is at rest." So, the initial momentum is 0 because the entire system is at rest. FINAL: "The 40kg boy jumps off at 4m/s and the 50kg girl jumps off at 2 m/s" Lets assume that the boy jumps from the left, and the girl from the right of the wagon, so the momentum of the boy is in -x direction and the girl's is in x direction. The wagon? We don't know yet. The final momentum is $$\vec{p}_{boy} + \vec{p}_{girl} + \vec{p}_{wagon} = -40 \cdot 4 \vec{e_x} + 50 \cdot 2 \vec{e_x} + 150 \cdot \vec{v_w}$$ The conservation of momentum says that $$\vec{p_{initial}} = \vec{p_{final}}$$, so $$0 = -40 \cdot 4 + 50 \cdot 2 + 150 \cdot v_w \Rightarrow 60 = 150 \cdot v_w \Rightarrow v_w = 2.5 m/s$$ And as v is positive, the wagon goes in the same direction the girl does. The other problem is the same.