Impact Analysis:
When a body of mass m strikes another body at rest of mass m/9, the impact can be analyzed using the principles of conservation of momentum and conservation of kinetic energy.

Conservation of Momentum:
According to the law of conservation of momentum, the total momentum before and after the impact should remain constant.
Let the initial velocity of the body with mass m be u1 and the initial velocity of the body with mass m/9 be 0.
After the impact, let the final velocity of both bodies be v.
Using the conservation of momentum, we can write:
m * u1 + (m/9) * 0 = m * v + (m/9) * v

Simplifying the equation:
m * u1 = (10m/9) * v

Conservation of Kinetic Energy:
According to the law of conservation of kinetic energy, the total kinetic energy before and after the impact should remain constant.
The initial kinetic energy of the system is given by:
KE_initial = (1/2) * m * u1^2

The final kinetic energy of the system is given by:
KE_final = (1/2) * m * v^2 + (1/2) * (m/9) * v^2

Fraction of Initial Kinetic Energy Transformed into Heat:
The fraction of the initial kinetic energy transformed into heat during the contact can be calculated by finding the difference between the initial and final kinetic energies and dividing it by the initial kinetic energy.

Let's calculate it step-by-step:

1. Calculate the final velocity (v):
From the conservation of momentum equation, we can solve for v:
m * u1 = (10m/9) * v
v = (9/10) * u1

2. Calculate the final kinetic energy (KE_final):
Substituting the value of v in the equation for KE_final, we get:
KE_final = (1/2) * m * ((9/10) * u1)^2 + (1/2) * (m/9) * ((9/10) * u1)^2
KE_final = (81/200) * m * u1^2 + (1/200) * m * u1^2
KE_final = (41/100) * m * u1^2

3. Calculate the fraction of initial kinetic energy transformed into heat:
The difference between the initial and final kinetic energies is:
ΔKE = KE_initial - KE_final
ΔKE = (1/2) * m * u1^2 - (41/100) * m * u1^2
ΔKE = (59/100) * m * u1^2

The fraction of the initial kinetic energy transformed into heat is given by:
Fraction = ΔKE / KE_initial
Fraction = (59/100) * m * u1^2 / [(1/2) * m * u1^2]
Fraction = 2 * (59/100)
Fraction = 1.18

Therefore, approximately 118% of the initial kinetic energy is transformed into heat during the contact.

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