You throw a small rock straight up with initial speed V0 from the edge of the roof of a building that is a distance H above the ground. The rock travels upward to a maximum height in time Tmax, misses the edge of the roof on its way down, and reaches the ground in time Ttotal after it was thrown. Neglect air resistance. If the total time the rock is in the air is three times the time it takes it to reach its maximum height, so Ttotal = 3Tmax, then in terms of H what must be the value of V0?

Question

You throw a small rock straight up with initial speed V0 from
the edge of the roof of a building that is a distance H above the ground.
The rock travels upward to a maximum height in time Tmax, misses the
edge of the roof on its way down, and reaches the ground in time Ttotal
after it was thrown. Neglect air resistance. If the total time the rock is in
the air is three times the time it takes it to reach its maximum height, so
Ttotal = 3Tmax, then in terms of H what must be the value of V0?

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