Let f be the force of friction and m be the mass of the body.

The frictional force exerted on a body moving on a rough horizontal surface and coming to a stop at a certain distance can be determined by considering the work-energy principle and the concept of kinetic friction.

Work-Energy Principle:
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the frictional force is responsible for reducing the kinetic energy of the body to zero. Therefore, the work done by the frictional force is equal to the initial kinetic energy of the body.

Kinetic Energy:
The kinetic energy (T) of an object is given by the equation T = (1/2)mv^2, where m is the mass of the object and v is its velocity.

Frictional Force:
The frictional force (f) exerted on the body is opposing its motion and can be determined using the equation f = μN, where μ is the coefficient of kinetic friction and N is the normal force acting on the body.

Explanation:
When the body is moving, it possesses kinetic energy (T). As the body comes to a stop, this kinetic energy is completely converted into work done by the frictional force. The work done by the frictional force is equal to the initial kinetic energy of the body.

Using the work-energy principle, we can write:

Work done by frictional force = Initial kinetic energy

f * y = (1/2)mv^2

Now, we can rearrange the equation to solve for the frictional force (f):

f = (1/2)mv^2 / y

This equation shows that the frictional force exerted on the body depends on the mass of the object (m), the velocity of the body (v), and the distance it takes to come to a stop (y).

The coefficient of kinetic friction (μ) between the body and the rough horizontal surface plays a significant role in determining the value of the frictional force. However, it is not explicitly mentioned in the given information. To calculate the exact value of the frictional force, the coefficient of kinetic friction or any additional information about the object's mass or velocity is needed.

In summary, the frictional force exerted on the body can be determined using the equation f = (1/2)mv^2 / y, where m is the mass of the object, v is its velocity, and y is the distance it takes to come to a stop.

Work done by the friction to stop the ball is equals to the loss of kinetic energy of the ball .1/2mv² = frictional force×distance moved(1/2mv²)/y = f