# A ball with a mass of 2 kg is rolling at 7 m/s and elastically collides with a resting ball with a mass of 4 kg. What are the post-collision velocities of the balls?

Jan 27, 2017

v1 = -2,33 m/s
v2 = 4,66 m/s

#### Explanation:

in the elastic collisions remain constant both the total kinetic energy both the momentum. Therefore:
1/2 m1 v1°^2 = 1/2 m1v1^2 + 1/2 m2 v2^2.
m1 v1° = m1 v1 + m2 v2 .
replacing the values in the equation of conservation of momentum, you find:
(1) $v 1 = 7 - 2 v 2$ .
that you put in the equation of conservation of energy.
Resolving the second degree equation, you find:
$6 v {2}^{2} - 28 v 2 = 0$.
then $V 2 = 0$ not useful and
$v 2 = 4 , 66 \frac{m}{s}$.
If You put in the (1), you find:
$v 1 = - 2 , 66 \frac{m}{s}$ i.e. the smaller ball comes back.

If you put the values in the equation of conservation of energy, you find that it is verified