A cart with mass 350 g moving on a frictionless linear air track at an initial speed of 1.2 m/s undergoes an elastic collision with an initi?

I'll use

M1V1+M2V2=M1V3+M2V4  conservation of momentum

and

1/2 M1V1^2 +1/2 M2V2^2 = 1/2 M1V3^2 + 1/2 M2V4^2

1/2 cancels

M1V1^2 + M2V2^2 =  M1V3^2 + M2V4^2  energy conserved

because this is an elastic collision

350(1.2) + 0 = 350(-0.59) + M2V4

M2V4 = 626.5

and

350(1.2^2) + 0 = 350(-059^2) + M2V4^2

M2V4^2 = 382.165

M2V4 V4 = 382.165

V4 = 382.165 / M2V4 = 382.165 /  626.5 = 0.61 m/s

so

M2 = M2V4 / V4 = 626.5 / 0.61 = 1027 g

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