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A bolt drops from the ceiling of a train car that is accelerating northward at a rate of 2.15 m/s2.

AWhat is the acceleration of the bolt relative to the train car?
BWhat is the acceleration of the bolt relative to the Earth?

Verified Answer :

AL2006

As soon as the bolt detaches from the ceiling, its northward acceleration
stops, and its downward acceleration begins.

Relative to the accelerating train car, the bolt has acceleration of
2.15 m/s² south, and 9.8 m/s² down.  When you puttum together,
the resultant of those two components is

                         √(2.15² + 9.8²)  =  √100.6625)  =  10.03 m/s²

      in the direction of  tan⁻¹(2.15/9.8)  =  12.4° south of straight down.

Relative to the Earth, the bolt has no horizontal acceleration and only vertical
acceleration of 9.8 m/s² straight down (toward the center of the Earth).

Note that I'm ignoring the centripetal acceleration toward the Earth's axis
due to daily rotation, and the centripetal acceleration toward the sun due
to the Earth's yearly revolution.  These are both relatively small, compared
to the acceleration of the train or of gravity.

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