Final answer:
The stopping force on a bullet can be calculated using the change in momentum and the distance it penetrates into the target. By considering the work done by the force and the initial kinetic energy of the bullet, the magnitude of the average stopping force can be determined.
Step-by-step explanation:
The question is concerned with calculating the magnitude and direction of the stopping force exerted on a bullet as it penetrates a target. To find the stopping force, we can use the concepts of impulse and momentum, where impulse equals the change in momentum. The bullet's initial momentum is given by its mass multiplied by its initial velocity. After the bullet stops inside the target, its final momentum is zero. The stopping force can then be calculated by dividing the negative change in momentum by the time taken to stop, which is determined by the bullet's penetration distance and initial velocity.
However, the exact time is not provided and thus can't be directly used to calculate the stopping force. Instead, we will use the work-energy principle. The work done by the stopping force is equal to the change in kinetic energy of the bullet. By calculating the initial kinetic energy and knowing that it has been entirely dissipated by the stopping force, we can find the work done by the stopping force. Dividing this work by the distance the bullet travels in the target gives us the magnitude of the average stopping force.