consider an elastic collision in one dimension that involves two objects 2.5 kg

Question

consider an elastic collision in one dimension that involves two objects 2.5 kg and 4.5 kg. the larger mass is initially at rest, and the smaller one has an initial velocity of 12 m/s. find the velocities of the two objects after the collision. Use mv+mv=mv+mv and 1/2mv^2+1/2mv^2=1/2mv^2+1/2mv^2 and the quadratic equation

Explanation / Answer

mv+m= mv+mv 2.5*12 + 4.5*0 = 2.5*v1 + 4.5*v2 or 30 = 2.5v1 + 4.5v2 or v2 = (30-2.5v1)/4.5 ----> (1) 1/2mv^2+1/2mv^2=1/2mv^2+1/2mv^2 mv^2+mv^2=mv^2+mv^2 2.5*12^2 + 4.5*0 = 2.5v1^2 + 4.5v2^2 or 360 = 2.5v1^2 + 4.5v2^2 substituting v2 from (1) 360 = 2.5v1^2 + 4.5[(30-2.5v1)/4.5]^2 or 360 = 2.5v1^2 + 200 + 1.39v1^2 - 33.3v1 or 3.89v1^2 - 33.3v1 -160 = 0 hence we get v1 = 12 v2 = 30-12/4.5 = 4

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