A particle is projected vertically upward and passes a point P at times t₁ and t₂, where t₂>t₁. The maximum height reached above P is:
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A particle is projected vertically upward and passes a point P at times t₁ and t₂, where t₂>t₁. The maximum height reached above P is:

G1 Physics · Accepted Answer

For vertical motion, y = ut − gt²/2. If the particle is at point P at times t₁ and t₂, the velocity at the midpoint time is zero: time at highest point = (t₁+t₂)/2. The time taken from P to the highest point is Δt = (t₂−t₁)/2. At P, the upward speed is speed at P = gΔt = g(t₂−t₁)/2. Hence height gained above P is h = speed at P²/(2g) = g(t₂−t₁)²/8.