A particle is projected vertically upward from the top of a tower of height H and hits the ground after time T. Its impact speed is:
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A particle is projected vertically upward from the top of a tower of height H and hits the ground after time T. Its impact speed is:

G1 Physics · Accepted Answer

Take upward as positive. Let initial speed be u and impact speed magnitude be V. Displacement to ground: −H = uT − gT²/2 ⇒ u = gT/2 − H/T. Impact velocity: v = u−gT = −[gT/2 + H/T]. Hence impact speed is V = gT/2 + H/T.