Physics problem...help would be great!?

Question

A wagon is coasting at a speed vA along a straight and level road. When ten percent of the wagon's mass is thrown off the wagon, parallel to the ground and in the foward direction, the wagon is brought to a halt. If the direction in which this mass is thrown is exactly reversed, but the speed of this mass relative to the wagon remains the same, the wagon accelerates to a new speed vB. Calculate the ratio vB/vA

the answer? = 2
how to get there? = NO CLUE

help? thanks a bunch

Answer 1

We know that kinetic energy Ke=0.5mV^2
When we throw the weight off the wagon in the same direction as the cart we are performing work against the cart motion (Third Law of Newton). Ad apposite when we throw the weight in reverse of motion we will add energy. Below are the governing equations. (this is similar to a rocket propulsion)
Equation 1
.5m1Va^2 – 0.5 m2Vx^2=0 where m1=.1m2
Equation 2
.5 m1Va^2 + 0.5 m2Vx^2=.5 m1Vb^2
Add these equations

m1Va^2=.5m1Vb^2
then

Vb/Va=2