A 0.30 kg object moving at 5.0 m/s to the right collides head-on with a 0.50 kg object moving at 2.0 m/s to the left. After the collision, the 0.30 kg object moves to the left at 1.0 m/s. What is the velocity of the 0.50 kg object immediately after the collision? (Take right as positive.)
Show the answer and explanation
Correct answer
A. 1.6 m/s to the right
Principle or equation
In an isolated system, total momentum is conserved: m1 v1i + m2 v2i = m1 v1f + m2 v2f.
Why this answer is correct
Let right be positive. Initial momenta: (0.30)(5.0) + (0.50)(-2.0) = 1.5 - 1.0 = 0.5 kg·m/s. After collision, the 0.30 kg object has momentum (0.30)(-1.0) = -0.30 kg·m/s. Let v be the final velocity of the 0.50 kg object. Then -0.30 + 0.50 v = 0.5, so 0.50 v = 0.8, v = 1.6 m/s. Positive means to the right.
Example
If a 1 kg object at 2 m/s hits a 2 kg object at rest and the 1 kg object rebounds at 1 m/s, then 2 = -1 + 2v, so v = 1.5 m/s.
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