Final Answer:
The person’s speed afterward will be greatest if (c) the ball misses the person entirely.
Step-by-step explanation:
When the ball is thrown horizontally at the person, the person will experience a force in the opposite direction due to the impact of the ball. According to Newton’s third law of motion, for every action, there is an equal and opposite reaction. If the person catches the ball or if the ball bounces off the person, there will be a transfer of momentum between the person and the ball, resulting in a decrease in the person’s speed. If the ball misses the person entirely, there will be no transfer of momentum, and thus the person’s speed afterward will be greatest.
In mathematical terms, when the ball is caught or bounces off the person, momentum is transferred to or from the person. Momentum is given by p = mv, where p is momentum, m is mass, and v is velocity. When momentum is transferred to or from the person, their velocity changes. However, if the ball misses the person entirely, there is no change in momentum for the person, and their speed remains unaffected.
In conclusion, based on Newton’s third law of motion and principles of momentum, it can be deduced that if the ball misses the person entirely, their speed afterward will be greatest.
So correct option is (c) the ball misses the person entirely.