Final velocities from head elastic head on collisions

AI Thread Summary
In a head-on collision between two equal mass balls, one moving at +3.00 m/s and the other at -2.00 m/s, the final velocities can be determined using the conservation of momentum and kinetic energy principles. The conservation of momentum ensures that the total momentum before and after the collision remains constant. The discussion highlights the use of the relative velocity formula, which relates the final velocities of the two balls to their initial velocities. By expressing one final velocity in terms of the other, simultaneous equations can be solved to find the final velocities. Ultimately, the final velocities are determined to be -2.00 m/s for Ball A and +3.00 m/s for Ball B.
henry3369
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Homework Statement


Ball A with velocity +3.00 m/s collides with ball B with equal mass traveling at -2.00 m/s. What is the velocity of each ball after the collision.

Homework Equations


Not sure.

The Attempt at a Solution


I know that momentum is conserved because, but solving the conservation of momentum equation yields two unknowns. I also tried impulse-momentum theorem and conservation of kinetic energy, but I'm not sure how that will help. The answer is Ball has velocity -2.00 m/s and ball B has velocity +3.00 m/s. Is there a formula to actually solve for this because they don't give you either of the final velocities.
 
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How did you use the law of conservation of kinetic energy?
 
If you can put one of the velocities of the balls after the collision in term of the other , you can solve this problem.
And the law of conservation of kinetic energy would help you.
 
Maged Saeed said:
If you can put one of the velocities of the balls after the collision in term of the other , you can solve this problem.
And the law of conservation of kinetic energy would help you.
Well in my book they gave me a formula for relative velocity which is V2f-V1f = -(V2i-V1i). And I have the initial velocities and which will leave me with two unknowns still. Do I have to relate this somehow to conservation of kinetic energy and solve simultaneous equations?
 
Ahh I got it. Thank you!
 

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