A stone is projected vertically upward. The time taken from projection to the highest point is t₁, while the time taken from the highest point to the ground is t₂. If the point of projection is at height H above ground, then:
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Question

A stone is projected vertically upward. The time taken from projection to the highest point is t₁, while the time taken from the highest point to the ground is t₂. If the point of projection is at height H above ground, then:

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G1 Physics · Accepted Answer

The upward speed is u=gt₁. Rise above the point of projection: upward rise = gt₁²/2. From the highest point, the stone falls from rest for time t₂, so total drop to ground is downward fall = gt₂²/2. But downward fall = H + upward rise. Therefore H = g(t₂²−t₁²)/2.