The pebble glides over the dome from the highest point without friction. The dome has the shape

The pebble glides over the dome from the highest point without friction. The dome has the shape of a sphere with a radius of 6 m. At what height from the top will the pebble come off the top?

Given:
R = 6 meters;
g = 10 N / kg;
vo = 0 m / s;
Find the separation height h;
Decision:
At the moment of separation: Еp = Еp + Еk;
m * g * R = m * g * h + m * v ^ 2/2;
Reduce by m, then we get:
g * R = g * h + v ^ 2/2;
Let’s find the speed:
m * acenstr = m * g * cos A;
acenstr = g * cosA;
Then, v ^ 2 = g * R * cos A, where cos A = h / R.
As a result, we got that v ^ 2 = g * R * cos A = g * R * h / R = g * h.
Substitute v ^ 2 = g * h in the expression g * R = g * h + v ^ 2/2, then we get:
g * R = g * h + v ^ 2/2;
g * R = g * h + g * h / 2;
Reduce by g, then we get:
R = h + h / 2;
R = h * (1 + 1/2) = 3/2 * h;
Hence, h = 2 * R / 3 = 2 * 6/3 = 12/3 = 4 meters.
Answer: 4 meters.