Will the Magnet Stick to the Car or Fall to the Ground?

[AirForceOne]

Homework Statement

A person throws out the back of a car a strong magnet that is attracted to the metal of the car. Will the magnet return and stick to the back of the car or fall to the ground? The initial velocity of the magnet is v=sqrt(5)i m/s. Treat the magnet/car interaction as an acceleration that act on the magnet equal to -a_mi, where a_m=10m/s^2 and L=1m. If the magnet hits the car at a point more than L below its starting height, it will encounter the plastic bumper and thus fail to stick.

The Attempt at a Solution

So I modeled the magnet's position then its acceleration, and then its position, getting:

However, I got y=1 for the magnet for all times t, which is not correct. If I understand correctly, the acceleration vector should be:

right?

Thanks.

 

[Spinnor]

Does the following look like a good start to solving the problem?

 

[RTW69]

Spinnor's diagram is very helpful. Hint: Where is the Vx=0 and at what time does that occur

 

[AirForceOne]

Thank you very much everyone. I understand it now.