A stone is thrown vertically upward. On its way up it passes point A with speed v, and point B, 6.2 m higher than A, with speed v/2. Calculate the maximum height reached by the stone above point B.

To calculate the maximum height reached by the stone above point B, we need to use the concept of conservation of energy.

Let's assume the initial position of the stone is at point A, and its final position is at the maximum height reached above point B. At point A, the stone has a certain velocity v, and at point B, it has a velocity of v/2. We need to find the maximum height difference between these two points.

The energy conservation principle states that the total mechanical energy of an object is constant, neglecting air resistance. In this case, the mechanical energy is the sum of kinetic energy (KE) and potential energy (PE).

At point A, the stone has only kinetic energy and no potential energy because it is at ground level. At point B, the stone has potential energy due to its height above the ground.

The equation for total mechanical energy can be expressed as:

E_total = KE + PE

At point A, the energy is given by:

E_A = KE_A + PE_A
= (1/2)mv^2 + 0 (since height is 0 at A)

At point B, the energy is given by:

E_B = KE_B + PE_B
= (1/2)mv^2/2 + mgh (since KE_B = (1/2)mv^2/2 and potential energy PE_B = mgh)

where m is the mass of the stone, g is the acceleration due to gravity, and h is the height at point B.

Since we know that energy is conserved, E_A = E_B, we can equate the two equations:

(1/2)mv^2 + 0 = (1/2)mv^2/2 + mgh

Simplifying this equation, we get:

v^2 = v^2/4 + 2gh

Multiplying the equation by 4 to eliminate the fraction:

4v^2 = v^2 + 8gh

Rearranging the equation, we find:

3v^2 = 8gh

Finally, solving for h (the maximum height above point B):

h = (3v^2)/(8g)

Substituting the given values, we can calculate the maximum height reached by the stone above point B.