A ball with a mass of 5kg is rolling at 1ms and elastically collides with a resting ball with a mass of 4kg. What are the post-collision velocities of the balls?

1 Answer
Jun 28, 2018

The post collisions velocities are =011ms1 and =1.411ms1

Explanation:

Since the collision is elastic, we have conservation of momentum

m1u1+m2u2=m1v1+m2v2

And conservation of kinetic energy

12m1u21+12m2u22=12m1v21+12m2v22

The mass the first ball is m1=5kg

The velocity of the first ball before the collision is u1=1ms1

The mass of the second ball is m2=4kg

The velocity of the second ball before the collision is u2=0ms1

The velocity of the first ball after the collision is =v1ms1

The velocity of the second ball after the collision is =v2ms1

Therefore,

51+40=5v1+4v2

4v2+5v1=5....................................(1)

12512+1240=125v21+124v22

4v22+5v21=5..............................(2)

Solving for v1 and v2 in equations (1) and (2)

From equation (1), v2=5(1v1)4

Substituting in equation (2)

5v21+4(5(1v1)4)2=5

4v21+5+5v2110v1=4

9v2110v1+1=0

v1=10±((10)2)4(9)(1)18=10±818

Therefore,

v1=1ms1 or v1=19=0.11ms1

v2=0ms1 or v2=109=1.11ms1

The first solutions are the initial conditions.

The post collisions velocities are =011ms1 and =1.411ms1