# Perfectly elastic collisoin with missing variables

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#1
Two balls labelled A and B have masses mA=1.0kg and mB=1.5kg. Initial velocities vAi=2.0m/s and vBi=-1.0m/s. If they collide in a perfetly elastic collision, what is vAf (the final speed of ball A) after the collision?

What I know so far is
Momentum is conserved, kinetic energy is conserved.

P1=0.5 kg m/s P1=P2
Ek1=2.75J Ek1=Ek2

P2= (mA x vAf) + (mB x vBf) Ek2= (0.5mA x vAf^2) + (0.5mB x vBf^2)

How do you solve this equation without knowing the final velocity of ball B? You have to relate the equation for momentum with the equation for kinetic energy, but I don't know how to do that without knowing the velocity of B.
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5 years ago
#2
(Original post by PatchworkTeapot)
Two balls labelled A and B have masses mA=1.0kg and mB=1.5kg. Initial velocities vAi=2.0m/s and vBi=-1.0m/s. If they collide in a perfetly elastic collision, what is vAf (the final speed of ball A) after the collision?

What I know so far is
Momentum is conserved, kinetic energy is conserved.

P1=0.5 kg m/s P1=P2
Ek1=2.75J Ek1=Ek2

P2= (mA x vAf) + (mB x vBf) Ek2= (0.5mA x vAf^2) + (0.5mB x vBf^2)

How do you solve this equation without knowing the final velocity of ball B? You have to relate the equation for momentum with the equation for kinetic energy, but I don't know how to do that without knowing the velocity of B.
Hey there,

Try forming two separate equations: one using the conservation of momentum and one using the conservation of kinetic energy. As these equations will both involve two unknowns (the final velocity of A and B), you should be able to solve the equations simultaneously. I hope that this has been helpful.
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