Question

In many old Western movies, a bandit is knocked back \(3 \mathrm{~m}\) after being shot by a sheriff. Which statement best describes what happened to the sheriff after he fired his gun? a) He remained in the same position. b) He was knocked back a step or two. c) He was knocked back approximately \(3 \mathrm{~m}\). d) He was knocked forward slightly. e) He was pushed upward.

Short answer

Answer: He was knocked back a step or two.

Step-by-step solution

Identify the relevant physical law

We can use Newton's third law of motion to analyze this situation. Newton's third law states that for every action, there is an equal and opposite reaction. This means that when the sheriff fires his gun, the force applied to the bullet also creates a force that is applied to the gun (and therefore the sheriff).

Assess the impact on the bandit

According to the exercise, the bandit is knocked back 3 meters after being shot. This means that the force of the bullet was enough to move the bandit, and therefore, a reaction force has been applied to the gun (and the sheriff).

Evaluate the possible statements

Now let's evaluate each statement provided: a) He remained in the same position: This statement is incorrect because the sheriff will experience a reaction force from shooting the gun, which will cause some movement. b) He was knocked back a step or two: This statement could be accurate since the reaction force might cause the sheriff some movement, but the distance might not be as dramatic as the 3 meters the bandit is knocked back. c) He was knocked back approximately 3 meters: This statement is incorrect because the sheriff's mass is likely to be much greater than the bullet's mass, so he won't be knocked back as far as the bandit. d) He was knocked forward slightly: This statement is incorrect because the direction of the reaction force is opposite to the direction of the bullet force. e) He was pushed upward: This statement is incorrect because there is no vertical force component in this scenario.

Choose the best statement

Based on the analysis of each statement in relation to Newton's third law of motion, the most accurate statement about what happened to the sheriff after he fired his gun is: b) He was knocked back a step or two.