Answer to Question 1
Answer: According to Newton's third law, the force of collision will be the same on both the bug and the car, but will act in opposite directions. The time during which the force acts is the same on both, so the impulses on the bug and the car will be equal in magnitude but opposite in direction. This means that each will undergo equal and opposite changes in momentum. It is important to stress that the momentum of car and the bug are not the same, but they change by the same amount The car loses as much momentum as the bug gains in the collision. Because of the small mass of the bug, its acceleration will be very large. Because of the large mass of the car, its acceleration (deceleration) will be unnoticeable.
Answer to Question 2
Answer: Both force and impulse on both the ball and the gun are equal and opposite. So they both undergo equal and opposite changes in momentum. Since they begin with no momentum, they have equal and opposite momentum as the ball fires and the gun recoils. Because the ball is less massive, it has the greater acceleration for the same force, and therefore moves faster.
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