Question

A 2.40-kg object is moving east at 4.00 m/s when it collides with a 6.00-kg object that is initially at rest. After the completely elastic collision, the larger object moves east at 2.29 m/s.

1)
What is the final velocity of the smaller object after the collision? Assume that the positive direction is to the east.(Express your answer to three significant figures.)

Answer 1

The final velocity of the smaller object after the collision is 1.725 meters per second to the west.

An elastic collision can be described by the principle of linear momentum conservation, whose model for these case is:

Principle of linear momentum conservation

$(2.40\,kg) \cdot \left(4\,\frac{m}{s} \right) = (2.40\,kg)\cdot v + (6\,kg)\cdot \left(2.29\,\frac{m}{s} \right)$

Where $v$ is the final velocity of the smaller object, in meters per second.

Then, the final velocity of the object is:

$v = -1.725\,\frac{m}{s}$

The final velocity of the smaller object after the collision is 1.725 meters per second to the west.

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