Posted by **James** on Tuesday, August 9, 2011 at 8:44pm.

Two balls have masses 44 kg and 86 kg. The

44 kg ball has an initial velocity of 80 m/s (to

the right) along a line joining the two balls

and the 86 kg ball is at rest. The 86 kg

ball has in initial velocity of −24 m/s. The

two balls make a head-on elastic collision with

each other.

44 kg

80 m/s

86 kg

−24 m/s

What is the final velocity of the 44 kg ball?

- physics -
**Damon**, Tuesday, August 9, 2011 at 8:54pm
You know the momentum is the same before and after

and

you know the kinetic energy is the same before and after

u = final velocity of 44 kg ball

v = final velocity of 86 kg ball

44*80 + 86* -24 = 44 u + 86 v

(1/2)44(80^2)+(1/2)86(24^2) =(1/2)44u^2+(1/2)86v^2

solve for u

- physics -
**drwls**, Tuesday, August 9, 2011 at 8:58pm
Since they have not told you the final velocity of at least one ball, you are going to have to use conservation of momentum AND kinetic energy to come up with answers. (Conservation of kinetic energy may not be a good assumption for some kinds of balls that do not bounce well, such as squash balls).

The math gets rather tedious, and I will leave it up to you. You can probably find the solution formula online.

A convenient way to solve this type of problem is to use a coordinate system that moves with the center of mass. In that system, each ball will simply reverse direction and keep the same speed. Then transform speeds back to lab coordinates.

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