Question

multiple select question
select all that apply
if two balls of different masses and velocities collide head on, which statements correctly describe their collision?

the forces that they exert on each other will be equal in magnitude and direction.
the impulses imparted on them will be equal in magnitude and direction.
the forces that they exert on each other will be equal in magnitude, but opposite in direction.
the impulses imparted on them will be equal in magnitude, but opposite in direction.

Explanation:

1. According to Newton's third law, the forces two objects exert on each other during interaction (like collision) are action - reaction pairs. So, the forces have equal magnitude and opposite direction. So the first statement is wrong and the third statement (The forces that they exert on each other will be equal in magnitude, but opposite in direction) is correct.
2. Impulse \(J = F\times t\). Since the forces \(F\) between the two balls are equal in magnitude and opposite in direction, and the time of interaction \(t\) is the same for both, the impulse \(J\) on each ball will be equal in magnitude (because \(|F_1\times t|=|F_2\times t|\) as \(|F_1| = |F_2|\)) and opposite in direction (because \(F_1=-F_2\), so \(J_1 = F_1\times t\) and \(J_2=F_2\times t=-F_1\times t=-J_1\)). So the second statement is wrong and the fourth statement (The impulses imparted on them will be equal in magnitude, but opposite in direction) is correct.

Answer:

C. The forces that they exert on each other will be equal in magnitude, but opposite in direction.
D. The impulses imparted on them will be equal in magnitude, but opposite in direction.