Question

I believe I am on the right track for this problem but I confused as to where I should go from here.
Q:A railroad flat car of weight W can roll without friction, left or right along a straight
horizontal track. Initially a woman of weight w is standing on the car, which is
moving to the right with speed V0 . What is the change in velocity of the car
(magnitude and direction) if the woman runs to the left so that her speed relative to
the car is Vrel just before she jumps off at the left end?

Answer 1

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Answer 2

We can solve this by looking at the momentums. Since we are worried about the change in velocity, we can start with the train car at rest (This is the same as boosting to the train's inertial reference frame. If you don't know what that means, don't worry about it :) )

So, initally, we have a train car and a woman sitting still. Their momentum is therefore zero, as p = mv, and v =0

Now, we make the lady run to the left and jump off with speed v_rel. Her weight is w, so her mass is w/g, where g is the acceleration due to gravity. The train cars mass is W/g, for the same reasons.

Since momentum is conserved, the woman's momentum to the left will equal the trains momentum to the right.
\[\frac{w}{g}v_{rel} = \frac{W}{g}v_{train}\]

Answer 3

"We can solve this by looking at the momentums. Since we are worried about the change in velocity, we can start with the train car at rest "

nice!