Oblique impact with one body coming to rest A 1 kg ball moves at 2 m/s and hits a stationary 2 kg ball in a straight-line impact. After collision, the 1 kg ball comes to rest. What is the velocity of the 2 kg ball just after impact?

Introduction / Context:
One-dimensional collisions are analyzed using conservation of linear momentum along the line of impact. Additional information such as the coefficient of restitution controls how kinetic energy changes, but if one body’s final velocity is given, momentum alone can determine the other.

Given Data / Assumptions:

• m1 = 1 kg with initial speed u1 = 2 m/s.
• m2 = 2 kg initially at rest (u2 = 0).
• After impact v1 = 0 (the 1 kg ball stops).
• Straight-line impact; external impulses negligible.

Concept / Approach:
Apply conservation of linear momentum along the line of impact: m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2. Insert the given values and solve for v2. Coefficient of restitution can be inferred afterwards if needed.

Step-by-Step Solution:

Verification / Alternative check:
If the collision had been perfectly elastic with these masses, v2 would have been 4/3 m/s and the lighter ball would not come to rest. Given v1 = 0, the computed v2 = 1 m/s is fully consistent with a partially elastic impact (e = 0.5).

Why Other Options Are Wrong:

• 0, 0.5 m/s: Violate momentum conservation with v1 = 0.
• 2.0 m/s, 3.0 m/s: Exceed the initial momentum capacity of the system.

Common Pitfalls:
Assuming “perfectly elastic” unless stated; always apply momentum first, then use any restitution data provided or implied.

Final Answer:
1.0 m/s