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(A) Let the initial velocity of $A$ be $u_A = 9 \ m/s$ and $B$ be $u_B = 0$. After the elastic collision between $A$ and $B$,let their velocities be $

Vedclass · Accepted Answer

$3$

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(A) Let the initial velocity of $A$ be $u_A = 9 \ m/s$ and $B$ be $u_B = 0$. After the elastic collision between $A$ and $B$,let their velocities be $v_A$ and $v_B$. Using conservation of linear momentum: $m(9) + 2m(0) = m v_A + 2m v_B \Rightarrow 9 = v_A + 2v_B$ (Equation $1$). Using the coefficient of restitution for elastic collision $(e=1)$: $v_B - v_A = e(u_A - u_B) = 1(9 - 0) = 9 \Rightarrow v_B - v_A = 9$ (Equation $2$). Adding Equation $1$ and Equation $2$: $3v_B = 18 \Rightarrow v_B = 6 \ m/s$. Now,$B$ makes a completely inelastic collision with $C$ (initially at rest). Let the final velocity of the combined mass $(B+C)$ be $v_C$. Using conservation of linear momentum: $2m(v_B) + 2m(0) = (2m + 2m)v_C$. $2m(6) = 4m v_C \Rightarrow 12m = 4m v_C \Rightarrow v_C = 3 \ m/s$.

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