Answer:
The final velocity of the student and the boat is 1.66 m/s
Explanation:
Law Of Conservation Of Linear Momentum
The total momentum of a system of bodies is conserved unless an external force is applied to it. The formula for the momentum of a body with mass m and velocity v is P=mv. If we have a system of bodies, then the total momentum is the sum of them all
[tex]P=m_1v_1+m_2v_2+...+m_nv_n[/tex]
Let's call [tex]m_s = 85\ kg[/tex] the mass of the physics student, [tex]m_b = 135\ kg[/tex] the mass of the boat, [tex]v_{so} =4.3\ m/s[/tex] the initial speed of the student, [tex]v_{bo} =0[/tex] the initial speed of the boat, [tex]v_f[/tex] the final speed of both, assumed common since they keep joined after the jump. Applying the law of conservation of momentum, being [tex]P_o\ and\ P_f[/tex] the initial and final momentum of the system, we have
[tex]P_o=P_f[/tex]
[tex]m_sv_{so}+m_bv_{bo}=(m_s+m_b)v_f[/tex]
Solving for [tex]v_f[/tex]
[tex]v_f=\frac{m_sv_{so}+m_bv_{bo}}{(m_s+m_b)}[/tex]
[tex]v_f=\frac{85(4.3)+0}{(85+135)}[/tex]
[tex]v_f=1.66 \ m/s[/tex]
The final velocity of the student and the boat is 1.66 m/s
