A ball with a mass of 3kg is rolling at 2ms and elastically collides with a resting ball with a mass of 4kg. What are the post-collision velocities of the balls?

1 Answer
Jun 26, 2017

The velocity of the first ball is =27ms1 and the second ball is =127ms1

Explanation:

Since the collision is elastic, there is conservation of linear momentum and conservation of kinetic energy.

m1u1+m2u2=m1v1+m2v2

12m1u21+12m2u22=12m1v21+12mv22

m1=3kg

m2=4kg

u1=2ms1

u2=0ms1

So,

32+40=3v1+4v2

3v1+4v2=6...............................(1)

12322+1240=123v21+124v22

3v21+4v22=12........................(2)

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

v2=63v14

3v21+4(63v14)2=12

12v21+3636v1+9v21=48

21v2136v112=0

7v2112v14=0

v1=12±122+44714

=12±1614

v1=2ms1 or v1=27=0.28ms1

We keep the second result v1=0.28ms1

v2=6+30.284=127=1.71

Verification

4127327=6