Three objects A,B,and C are kept in a straigh | vedclass

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(C) Step $1$: Elastic collision between $A$ and $B$.Let $v_A = 9 \ m/s$ and $v_B = 0$. After the collision,let the velocities be $v_A'$ and $v_B'$.By

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$4$

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(C) Step $1$: Elastic collision between $A$ and $B$.Let $v_A = 9 \ m/s$ and $v_B = 0$. After the collision,let the velocities be $v_A'$ and $v_B'$.By conservation of momentum: $m(9) + 2m(0) = m v_A' + 2m v_B' \Rightarrow 9 = v_A' + 2v_B'$.By the coefficient of restitution for an elastic collision $(e=1)$: $v_B' - v_A' = e(v_A - v_B) = 1(9 - 0) = 9 \Rightarrow v_B' - v_A' = 9$.Adding the two equations: $(v_A' + 2v_B') + (v_B' - v_A') = 9 + 9 \Rightarrow 3v_B' = 18 \Rightarrow v_B' = 6 \ m/s$.Step $2$: Completely inelastic collision between $B$ and $C$.Let $v_B' = 6 \ m/s$ and $v_C = 0$. After the collision,$B$ and $C$ move together with velocity $v_f$.By conservation of momentum: $2m(v_B') + m(0) = (2m + m)v_f \Rightarrow 2m(6) = 3m v_f \Rightarrow 12 = 3v_f \Rightarrow v_f = 4 \ m/s$.Thus,the final speed of object $C$ is $4 \ m/s$.

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