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

of the student is 4.3 m/s as she leaves the dock, what is the final velocity of the student and the boat?

Answer 1

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

Step-by-step 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=(m_sv_(so)+m_bv_(bo))/((m_s+m_b))`

`v_f=(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