Initial Analysis:
Given that the body loses half of its velocity on penetrating 3 cm in a wooden block, we can use the concept of energy conservation to calculate how much more it will penetrate before coming to rest.

Calculating Initial Velocity:
Let the initial velocity of the body be V. When the body penetrates 3 cm in the wooden block, it loses half of its velocity, so its final velocity becomes V/2.

Using Energy Conservation:
By using the principle of energy conservation, we can calculate the work done by the body in penetrating the wooden block. This work is equal to the initial kinetic energy of the body.

Calculating Work Done:
The work done by the body is given by the formula W = Fd, where F is the force opposing the motion and d is the distance penetrated. Since the body is coming to rest, the work done is equal to the initial kinetic energy of the body.

Calculating Distance Penetrated:
Now that we have the work done by the body, we can calculate how much more distance the body will penetrate before coming to rest. This can be done by equating the work done to the initial kinetic energy of the body and solving for the distance.

Final Calculation:
After calculating the distance penetrated by the body before coming to rest, we can determine the total distance penetrated by adding the initial 3 cm. This will give us the final answer to how much more the body will penetrate before coming to rest.