In a 1-dimensional elastic collision between 2 objects, Object A and Object B, v

Question

In a 1-dimensional elastic collision between 2 objects, Object A and

Object B, vA, initial = 5 m/s and vB, initial = -12 m/s. If the masses of the 2 objects are

related such that: mA = 3mB, what will vA, final and vB, final be?

Explanation / Answer

from momentum conservation ; mA* vA +mB*vB =mA *vA' +mB* vB' => 3mB *5 +mB *(-12) = 3mB *vA' +mB *vB' => mB(3vA' +vB') = 3mB => 3vA' +vB' = 3 in an elastic collision, sum of K.E. of the system is constant after collision. 0.5mA*5^2 +0.5mB* (-12)^2 = 0.5*mA *vA'^2 +0.5*mB*vB'^2 => 75mB +144mB = 3mB*vA'^2 +mB*vB'^2 => 3vA'^2 +vB'^2 =219 => 3[(3-vB')/3]^2 +vB'^2 =219 => vA' =13.5 m/s , vB' =-37.5 m/s or vA' =-12m/s , vB' = 39 m/s

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