A block of mass m1 = 5.0 kg is released from A, at a height h = 9.0 m. It makes a head-on elastic collision at B with a block of mass m2 = 11.0 kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision.

the track is frictionless

To calculate the maximum height to which block m1 rises after the collision, we can use the principle of conservation of mechanical energy. The total mechanical energy of the system (m1 + m2) remains constant throughout the process.

Since the track is frictionless, we can ignore any dissipative forces, and the only form of energy involved is gravitational potential energy. The initial energy of block m1 at point A is given by its gravitational potential energy:

E_initial = m1 * g * h

Where:
m1 = mass of block 1 (5.0 kg)
g = acceleration due to gravity (9.8 m/s²)
h = height (9.0 m)

After the collision, block m1 will reach a maximum height, which we will denote as "H." At this maximum height, all of the block's initial gravitational potential energy will be converted into potential energy. Since the collision is elastic, there is no loss of energy due to deformation or other internal processes.

At the maximum height, the total energy of the system is the sum of the potential energy of block m1 and zero potential energy for block m2 (since it is at rest at this point):

E_final = m1 * g * H + 0

According to the conservation of mechanical energy, the initial energy of the system is equal to its final energy:

E_initial = E_final

Therefore, we can set up the equation:

m1 * g * h = m1 * g * H + 0

Simplifying the equation, we get:

m1 * g * h = m1 * g * H

Now we can solve for H:

H = (m1 * g * h) / (m1 * g)

By substituting the given values into the equation, we can find the maximum height to which block m1 rises after the collision.