A ball is thrown vertically down from a height of 2 meters. Reflecting absolutely resiliently from the horizontal surface

A ball is thrown vertically down from a height of 2 meters. Reflecting absolutely resiliently from the horizontal surface, the ball rises to a height of 4 meters. How fast did you throw the ball?

From the law of conservation of energy:
mgh = (mv ^ 2) / 2
gh = v ^ 2/2
v ^ 2 = 2gh
Now let’s write down the difference of the squares of the speeds. Let v_01 be the initial velocity of the body at the height h1, v_0 the velocity of the body on the surface, v_2 the velocity of the body at the height h2. Then
(v_0) ^ 2 – (v_01) ^ 2 = 2gh1
(v_0) ^ 2 = 2gh ^ 2
Substitute: instead of (v0) ^ 2
(v_01) ^ 2 = 2gh ^ 2 – 2gh ^ 1
(v_01) = √ (2g (h1 – h2)) = √40 = 6.3 (m / s)
Answer: 6.3 (m / s)