Does a car accelerate horizontally when a box is shot vertically upward from it?

[ketsalex]

A car with mass M1,with a box upon it of mass M2 moves with constant speed v.(there is no friction).If the box is shot vertically with speed v1 relative to the car then the final speed of the car will remain orizontial?or it will be floating downwards in relation to an observer that is at rest?

 

[sophiecentaur]

Without suspension it would be the car plus the Earth which move 'downwards' with a vanishingly small vertical velocity.
With suspension, the vertical speed of the car would be, initually, according to the momentum conservation formula,
m1 v1 = m2v2
until the springs slowed it down etc..