A particle A is projected vertically upward from the ground with speed u. Simultaneously, a platform at height H starts moving downward from rest with constant acceleration a, where 0<a<g. The minimum u for which A just meets the platform is:
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Question

A particle A is projected vertically upward from the ground with speed u. Simultaneously, a platform at height H starts moving downward from rest with constant acceleration a, where 0<a<g. The minimum u for which A just meets the platform is:

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G1 Physics · Accepted Answer

Take upward as positive. Particle A: position of A = ut − gt²/2. Platform: platform position = H − at²/2. For a meeting, ut − gt²/2 = H − at²/2. Thus (g−a)t²/2 − ut + H = 0. For the minimum u that still allows a meeting, this quadratic has exactly one real root, so its discriminant is zero: u² − 2(g−a)H = 0. Hence minimum u = √[2(g−a)H].