Explanations & Calculations
"\\qquad\\qquad\n\\begin{aligned}\n\\small E_p +E_k &= \\small E_p+E_k \\\\\n\\small(m_1gh +0) &=\\small(0+\\frac{1}{2}m_1u^2)\\\\\n\\small u &= \\small\\sqrt{2gh}\\\\\n&= \\small \\sqrt{2\\times9.8ms^{-2}\\times5m}\\\\\n&= \\small 7\\sqrt{2}ms^{-1}\n\\end{aligned}"
"\\qquad\\qquad\n\\begin{aligned}\n\\small m_1u +m_20 &= \\small (m_1+m_2)v\\\\\n\\small v &= \\small \\frac{m_1u}{m_1+m_2}\\\\\n&= \\small \\frac{5kg\\times7\\sqrt{2}ms^{-1}}{(5kg+10kg)}\\\\\n&= \\small \\frac{7\\sqrt{2}}{3}ms^{-1}\n\\end{aligned}"
"\\qquad\\qquad\n\\begin{aligned}\n\\small E_{k(m_1+m_2)} &= \\small \\frac{1}{2}(m_1+m_2)v^2\\\\\n\\end{aligned}"
And,
"\\qquad\\qquad\n\\begin{aligned}\n\\small E_k+E_p &= \\small E_k+E_p\\\\\n\\small \\frac{1}{2}(m_1+m_2)v^2+0&=\\small 0+(m_1+m_2)gh\\\\\n\\small h &= \\small \\frac{v^2}{2g}\\\\\n\\small h &= \\small \\frac{(\\frac{7\\sqrt{2}}{3}ms^{-1})^2}{2\\times9.8ms^{-2}}\\\\\n&= \\small \\bold{0.56m}\n\\end{aligned}"
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