Problem

The key insight is that the last 2 seconds of upward motion means the final 2 seconds before the particle returns to its starting height—so you need to find the total flight time first, then work backwards. Once you know when the particle lands, use the kinematic equation $s = ut + \frac{1}{2}gt^2$ for that final 2-second interval. The beauty is that the initial velocity $u$ cancels out, leaving you with a distance that depends only on $g$ and the time interval.

The key insight is that the last 2 seconds of upward motion means the final 2 seconds before the particle returns to its starting height—so you need to find the total flight time first, then work backwards. Once you know when the particle lands, use the kinematic equation $s = ut + \frac{1}{2}gt^2$ for that final 2-second interval. The beauty is that the initial velocity $u$ cancels out, leaving you with a distance that depends only on $g$ and the time interval.