Question

A 20 kg child sits in a 25 kg boat at rest, and throws a 14 kg package horizontally from the boat at a speed of 8 m/s to the left. What is the velocity of the boat and child after this? (Make to the right positive)

Answer 1

Given data:

* The mass of the child is m_1 = 20 kg.

* The mass of the boat is m_2 = 25 kg.

* The mass of the package is m_3 = 14 kg.

* The velocity of the package is v = 8 m/s.

Solution:

According to the law of conservation of momentum, the momentum of the boat along with the child towards the right is equal to the momentum of the package towards the left.

Thus,

`(m_1+m_2)v^(\prime)=m_3v`

Substituting the known values,

`\begin{gathered} (20+25)v=14*8 \\ 45v=112\text{ } \\ v=(112)/(45) \\ v=2.49\text{ m/s} \end{gathered}`

Thus, the velocity of the boat and child towards the right is 2.49 meters per second.