A stone thrown almost vertically up from the surface of the earth, 3 seconds after the throw fell on the roof of a house 15 m high.

A stone thrown almost vertically up from the surface of the earth, 3 seconds after the throw fell on the roof of a house 15 m high. Find the initial velocity of the stone. Disregard air resistance.

Let’s write down the general formula:
h = v0t – gt ^ 2/2
After 3 s, the height h became 15m. Then v0:
v0 = [h + (gt ^ 2/2)] / t
Let’s substitute:
v0 = [15 + (10 * 3 ^ 2) / 2] / 3
v0 = 20 (m / s)
Answer: v0 = 20 (m / s)