Respuesta :
We are given that the Titanic hit an iceberg half of its mass. To determine the velocity of the iceberg after the collision we have to do a balance of momentum:
[tex]m_Tv_{1T}+m_Iv_{1I}=m_Tv_{2T}+m_Iv_{2I}[/tex]Where:
[tex]\begin{gathered} m_T=\text{ mass of the titanic} \\ v_{1T}=\text{ initial velocity of the titanic} \\ m_I=\text{ mass of the Iceberg} \\ v_{1I}=\text{ initial velocity of the iceberg} \\ v_{2T}=\text{ final velocity of the titanic} \\ v_{2I}=\text{ final velocity of the iceberg} \end{gathered}[/tex]Now, since the iceberg is initially at rest, we have:
[tex]v_{1I}=0[/tex]Substituting in the balance of momentum we get:
[tex]\begin{gathered} m_Tv_{1T}+m_I(0)_{}=m_Tv_{2T}+m_Iv_{2I} \\ m_Tv_{1T}=m_Tv_{2T}+m_Iv_{2I} \end{gathered}[/tex]We are given that the mass of the iceberg is half of the mass of the Titanic, therefore, we have:
[tex]m_I=\frac{m_T}{2}[/tex]Substituting in the balance of momentum:
[tex]m_Tv_{1T}=m_Tv_{2T}+\frac{m_T}{2}v_{2I}[/tex]Now, we can cancel out the mass of the Titanic:
[tex]v_{1T}=v_{2T}+\frac{1}{2}v_{2I}[/tex]Now we solve for the final velocity of the iceberg. We subtract the final velocity of the Titanic from both sides:
[tex]v_{1T}-v_{2T}=\frac{1}{2}v_{2I}[/tex]Now we multiply both sides by 2:
[tex]2(v_{1T}-v_{2T})=v_{2I}[/tex]Substituting the values we get:
[tex]2(11.3\frac{m}{s}-3.1\frac{m}{s})=v_{2I}[/tex]Solving the operations we get:
[tex]16.4\frac{m}{s}=v_{2I}[/tex]Therefore, the final velocity of the iceberg is 16.4 meters per second.
