A stone is projected vertically upward from the top of a tower and reaches the ground after time T with impact speed V. The height H of the tower is:
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A stone is projected vertically upward from the top of a tower and reaches the ground after time T with impact speed V. The height H of the tower is:

G1 Physics · Accepted Answer

Take upward as positive. At impact, −V = u − gT ⇒ u = gT − V. The displacement from the top of the tower to the ground is −H: −H = uT − gT²/2. Substitute u: −H = (gT−V)T − gT²/2 = gT²/2 − VT. Therefore H = VT − gT²/2.