Question

objects a and b collide in an isolated system. the vector arrows represent the before- and after-collision momentum of objects a and b. which vector represents the momentum of object b after the collision?
before collision after collision
p_b p_a p_b = ??? p_a
a b c d
p_b p_b p_b p_b
e f g h
p_b p_b p_b p_b

Explanation:

Step1: Define momentum conservation

In an isolated system, total momentum is conserved:
$$\vec{p}_{A,\text{initial}} + \vec{p}_{B,\text{initial}} = \vec{p}_{A,\text{final}} + \vec{p}_{B,\text{final}}$$

Step2: Assign magnitude/direction values

Let right be positive. Let each tick = $p$.

• $\vec{p}_{A,\text{initial}} = -p$ (left direction)
• $\vec{p}_{B,\text{initial}} = +3p$ (right, 3 ticks)
• $\vec{p}_{A,\text{final}} = +p$ (right, 1 tick)

Step3: Solve for final B momentum

Rearrange conservation law:
$$\vec{p}_{B,\text{final}} = \vec{p}_{A,\text{initial}} + \vec{p}_{B,\text{initial}} - \vec{p}_{A,\text{final}}$$
Substitute values:
$$\vec{p}_{B,\text{final}} = -p + 3p - p = +p$$
This is a rightward vector with 1 tick.

Answer:

A. $\vec{p}_B$ (rightward, 1 tick vector)