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Bounce for a moving car

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The car with its passengers is traveling along a horizontal road when it suddenly runs onto a new piece of road surface, raised 5.5 cm above the old surface. Assume that this suddenly raises the wheels and the bottom ends of the springs through 5.5 cm before the body of the car begins to move upward. In the ensuing rebound, are the passengers thrown clear of their seats? To answer this, consider the maximum acceleration of the resulting simple harmonic motion, assuming the passengers do remain in their seats.
a) What is the maximum downward acceleration of the vehicle after it bounces? Enter the maximum acceleration of the car and passengers, assuming they do remain seated, as your first answer (without a sign),

b) Will the passengers would be thrown clear of their seats. just tell yes or no.

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Solution Preview

The statement of the problem fails to say that there are no springs IN THE SEATS themselves and the muscles of the passengers remain TOTALLY RELAXED.
However the formulation of the problem is such that it looks like the teacher just forgot to mention this.
We shall therefore assume that there are no springs in the seats or anywhere except the springs connecting the wheels to the body of the car and the muscles of the passengers remain totally relaxed.

In this case, the answers are (a) g (=9.8m/s^2) and (b) No.

Here is the explanation.

First, let us consider a simplified situation of just a car with no passengers and some arrangement by which the wheels of the car CANNOT LEAVE THE ROAD, held to it ...

Solution Summary

The solution calculates the acceleration and what would happen to the passengers when the car hits a bump.