Question

A 85-kg physics student jumps from a dock into a 135 kg boat that is at rest by the dock. If the velocity

Answer 1

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

$P=m_1v_1+m_2v_2+...+m_nv_n$

Let's call $m_s = 85\ kg$ the mass of the physics student, $m_b = 135\ kg$ the mass of the boat, $v_{so} =4.3\ m/s$ the initial speed of the student, $v_{bo} =0$ the initial speed of the boat, $v_f$ the final speed of both, assumed common since they keep joined after the jump. Applying the law of conservation of momentum, being $P_o\ and\ P_f$ the initial and final momentum of the system, we have

$P_o=P_f$

$m_sv_{so}+m_bv_{bo}=(m_s+m_b)v_f$

Solving for $v_f$

$v_f=\frac{m_sv_{so}+m_bv_{bo}}{(m_s+m_b)}$

$v_f=\frac{85(4.3)+0}{(85+135)}$

$v_f=1.66 \ m/s$

The final velocity of the student and the boat is 1.66 m/s