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?

1 Answer
Jan 27, 2017

Answer:

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) #v1= 7 -2 v2 # .
that you put in the equation of conservation of energy.
Resolving the second degree equation, you find:
#6v2^2 -28 v2 =0#.
then #V2=0# not useful and
#v2 = 4,66 m/s#.
If You put in the (1), you find:
#v1= -2,66 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