# A ball with a mass of # 6 kg# is rolling at #16 m/s# and elastically collides with a resting ball with a mass of # 1 kg#. What are the post-collision velocities of the balls?

##### 1 Answer

#### Answer:

These momentum problems are the first in physics where you're responsible for managing a (relatively) large number of variables.

#### Explanation:

Recall,

Which is derived starting from,

(a restatement of the law of conservation of momentum and energy, respectively).

Then, by factoring out (2), and dividing the expansion by (1).

From here, since ball B is at rest, it's easy. Consider,

Now, consider the conformity with the law of conservation of momentum, and substituting this variable in,

and by extension,

From this calculation, we can understand that:

**In perfectly elastic collisions, all of the energy or momentum is transferred perfectly from one body to the other, if one is at rest.**