User:Gfreeman9


 * $$ \mathrm{initial\; velocity\;} v_i = \frac{(\mathrm{mass\; of\; the\; bullet}\; (m_1) + \mathrm{mass\; of\; the\; can\;} (m_2)) * \mathrm{distance}\;x\;(x\;\mathrm{in\;the\;diagram})}{\mathrm{mass\;of\; the\; bullet\;} (m_1) * \sqrt{\frac{2*\mathrm{distance}\;y(y\; \mathrm{in\; the\; diagram})}{g}}} $$.


 * $$ m_1v_{1,i}+m_2v_{2,i} = (m_1+m_2)v_f \,$$.


 * $$y = \frac{1}{2}gt^2 $$


 * $$\sqrt{\frac{2y}{g}}= t \,$$


 * $$v_ft=x \,$$


 * $$ x = v_f\sqrt{\frac{2y}{g}}$$


 * $$v_f = \frac{x}{\sqrt{\frac{2y}{g}}}$$


 * $$m_1v_{1,i} + m_2v_{2,i} = \frac{(m_1+m_2)x}{\sqrt{\frac{2y}{g}}}$$


 * $$m_1v_{1,i} + 0 = \frac{(m_1+m_2)x}{\sqrt{\frac{2y}{g}}} $$


 * $$v_{1,i} = \frac{(m_1+m_2)x/\sqrt{\frac{2y}{g}}}{m_1}$$


 * $$v_{1,i} = \frac{(m_1+m_2)x}{m_1\sqrt{\frac{2y}{g}}}$$