A 0.20 kg ball moving at 4.0 m/s to the right collides head-on with a 0.60 kg ball moving at 2.0 m/s to the left. If the collision is perfectly inelastic and the balls stick together, what is the velocity of the combined mass immediately after the collision? (Take right as positive.)
Show the answer and explanation
Correct answer
B. 0.50 m/s to the left
Principle or equation
In a perfectly inelastic collision, momentum is conserved: m1v1 + m2v2 = (m1 + m2)v_final.
Why this answer is correct
Take right as positive. Initial momentum = 0.20 × 4.0 + 0.60 × (-2.0) = 0.8 - 1.2 = -0.4 kg·m/s. Total mass = 0.80 kg. v_final = -0.4 / 0.80 = -0.50 m/s, i.e., 0.50 m/s to the left.
Example
A 1.0 kg object moving at 3.0 m/s right collides and sticks to a 2.0 kg object moving at 1.0 m/s left. Final velocity = (3.0 - 2.0)/3.0 = 0.33 m/s right.
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