Option 1:
Right as positive:
\left.\begin{array}{rl}\Sigma p_i & =\sum p_f \\ m_Av_{Ai}+m_BV_{Bi} & =m_Av_{Af}+m_Bv_{Bf} \\ m_Av_{Ai}+m_Bv_{Bi} & =\left(m_A+m_B\right)v_f\end{array}\right\}Anyone
(7,2)(0,4)+(0)=(7,2+5,3) v_f
v_{\mathrm{f}}=0,23 \mathrm{~m} \cdot \mathrm{s}^{-1}
OR
Left as positive:
\left.\begin{array}{rl}\sum p_i & =\sum p_f \\ m_Av_{Ai}+m_Bv_{Bi} & =m_Av_{Af}+m_Bv_{Bf} \\ m_Av_{Ai}+m_Bv_{Bi} & =\left(m_A+m_B\right)v_f\end{array}\right\}Anyone
(7,2)(-0,4)+(0)=(7,2+5,3) v_f
v_f=-0,23
\therefore \mathrm{v}_{\mathrm{f}}=0,23 \mathrm{~m} \cdot \mathrm{s}^{-1}
OR
Option 2:
Right as positive:
\left.\begin{array}{rl}\Delta\mathrm{p}_{\text{trolley }} & =-\Delta\mathrm{p}_{\text{trolley }}\mathrm{B} \\ \mathrm{m}_{\mathrm{A}}\left(\mathrm{v}_{\mathrm{Af}}-\mathrm{v}_{\mathrm{Ai}}\right) & =-\mathrm{m}_{\mathrm{B}}\left(\mathrm{v}_{\mathrm{Bf}}-\mathrm{v}_{\mathrm{Bi}}\right)\end{array}\right\}Anyone
(7,2)\left(v_f-0,4\right)=-(5,3)\left(v_f-0\right)
v_f=0,23 \mathrm{~m} \cdot \mathrm{s}^{-1}
OR
Left as positive:
\left.\begin{array}{rl}\Delta\mathrm{p}_{\text{trolley }} & =-\Delta\mathrm{p}_{\text{trolley }\mathrm{B}} \\ \mathrm{m}_{\mathrm{A}}\left(\mathrm{v}_{\mathrm{Af}}-\mathrm{v}_{\mathrm{Ai}}\right) & =-\mathrm{m}_{\mathrm{B}}\left(\mathrm{v}_{\mathrm{Bf}}-\mathrm{v}_{\mathrm{Bi}}\right)\end{array}\right\}Anyone
(7,2)\left(v_f+0,4\right)=-(5,3)\left(v_f-0\right)
v_f=-0,23
\therefore \mathrm{v}_{\mathrm{f}}=0,23 \mathrm{~m} \cdot \mathrm{s}^{-1}
Teacher tip
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