Asked by jay
Ball A, moving with an initial speed of 3 m/s, has a head-on collision with another ball B at rest, which is twice as massive as A . What are the final velocities of A and B if the collision is elastic?
Answers
Answered by
Jennifer
In an elastic collision, both momentum and kinetic energy are conserved.
Conservation of momentum
m*3 = m*vA + 2m*vB
or
3 = vA + 2*VB
where vA is the speed of A, and vB is the speed of B
Conservation of kinetic energy:
1/2*m*3^2 = 1/2*m*vA^2 + 1/2*2*m*vB^2
9 = vA^2 + 2*vB^2
You have two equations with two unknowns:
3 = vA + 2*VB
9 = vA^2 + 2*vB^2
Use algebra to solve for vA and vB
Conservation of momentum
m*3 = m*vA + 2m*vB
or
3 = vA + 2*VB
where vA is the speed of A, and vB is the speed of B
Conservation of kinetic energy:
1/2*m*3^2 = 1/2*m*vA^2 + 1/2*2*m*vB^2
9 = vA^2 + 2*vB^2
You have two equations with two unknowns:
3 = vA + 2*VB
9 = vA^2 + 2*vB^2
Use algebra to solve for vA and vB
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