A baggage cart full of luggage is coasting at a speed v A across the airport tax

Question

A baggage cart full of luggage is coasting at a speed vA across the airport taxiway. When twenty-two percent of the mass of the cart and luggage is thrown off the cart, parallel to the ground and in the forward direction, the cart 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 cart remains the same, the cart accelerates to a new speed vB. Calculate the ratio vB/vA.

THE PREVIOUS POSTS OF THIS QUESTION ANSWERS ARE INCORRECT. Thanks

Explanation / Answer

MVA = (0.22)*M*V
=> V = (1/0.22)*VA

Now, speed of luggage w.r.t. cart is V - VA = (1/0.22)*VA - VA =(0.78/0.22)* VA

MVA = (M-0.22M)*VB - 0.22M*(V')
Now, new speed of luggage w.r.t. cart is V' + VA = (0.78/0.22)* VA ===> V' = (0.56/0.22)*VA
VA = 0.78*VB - 0.22*V'
VA = 0.78*VB - 0.22*(0.56/0.22)*VA
1.56*VA = 0.78*VB
=> VB / VA   = 2

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