A ball with a mass of 3kg is rolling at 8ms and elastically collides with a resting ball with a mass of 4kg. What are the post-collision velocities of the balls?

1 Answer
Jan 5, 2018

The post collision velocities are =1.14ms1 and =6.86ms1

Explanation:

In an elastic collision, there is conservation of momentum and conservation of kinetic energies.

m1u1+m2u2=m1v1+m2v2

12m1u21+12m2u22=12m1v21+12m2v22

Here,

The masses are

m1=3kg

and m2=4kg

The initial velocities are

u1=8ms1

and u2=0ms1

38+40=3v1+4v2, , 3v1+4v2=24........(1)

12382+12402=123v21+124v22

3v21+4v22=192.............................(2)

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

From (1), v2=243v14

Substituting is (2)

3v21+4(243v14)2=192

12v21+(243v1)2=768

12v21+576144v1+9v21=768

21v21144v192=0

7v2148v64=0

v1=48±(48)247(64)27

=48±409614

=48±6414

So,

v1=(48+6414)=8ms1, , v2=0ms1

This is the initial conditions.

or

v2=(486414)=1.14ms1, , v2=6.86ms1