A container accelerates horizontally with constant acceleration a. A particle is released inside it and then moves freely under gravity. Relative to the container, the particle behaves as if it were in a uniform effective gravitational field of magnitude:
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Question

A container accelerates horizontally with constant acceleration a. A particle is released inside it and then moves freely under gravity. Relative to the container, the particle behaves as if it were in a uniform effective gravitational field of magnitude:

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G1 Physics · Accepted Answer

In the non-inertial frame of the container, the particle experiences gravity g downward and pseudo acceleration a opposite the container's acceleration. These are perpendicular, so effective gravitational acceleration has magnitude g_eff = √(g²+a²).