The ball is pushed up the inclined plane at a speed V0. Moving uniformly

The ball is pushed up the inclined plane at a speed V0. Moving uniformly, it rises up and rolls down. What is its average ground speed?

Since the condition of the problem is not specified, we assume that V0 is the initial velocity of the ball. That is, some force imparted the speed V0 to the ball, and then ceased to act on the ball. Then, according to the law of conservation of energy:

At the beginning of the upward movement, the speed of the ball is V0;

At the top point, the speed of the ball is 0;

At the lowest point, the speed of the ball is V0.

Let the length of the plane from the beginning to the top point be equal to l.

Then, we have that:

v0 = g * t.

t = v0 / g.

The ascent time and descent time will be the same.

I.e:

Vav = 2 * l / (2 * t) = l / t = l / (v0 / g) = l * g / v0.

Since l = g * t ^ 2/2 = v0 ^ 2 / (2 * g), then:

Vcp = v0 ^ 2 * g / (2 * v0 * g) = v0.

Answer: the average ground speed will be v0.