A wagon is coasting at a speed Va along a straight and level road

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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 forward 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 acclerates to a new speed Vb. What is the ratio Vb/Va.

Assume the mass of the wagon is m. then the mass thrown off is 0.1m, and the mass left for the wagon is 0.9m.

According to conservation of momentum,
(1) when it was thrown off in the forward direction, the wagon stops,

, where vf is the speed of the mass thrown off the wagon
Then vf = 10 Va

(2) if the 10%m is thrown off in the opposite direction with speed 10Va, then

So the ratio is 20/9.