Question

A child in a boat throws a 5.75-kg package out horizontally with a speed of 10.0 m/s. The mass of the child is 23.6kg and the mass of the boat is 37.6kg. Calculate the velocity of the boat immediately after, assuming it was initially at rest. v′A=?

Answer 1

Answer on Question #48042, Physics, Mechanics | Kinematics | Dynamics

Question:

A child in a boat throws a 5.75-kg package out horizontally with a speed of 10.0 m/s. The mass of the child is 23.6kg and the mass of the boat is 37.6kg. Calculate the velocity of the boat immediately after, assuming it was initially at rest. v'A=?

Answer:

The law of conservation of momentum:

$$m_p v + (M + m) u = 0$$ $$u = - \frac {m _ {p}}{m + M} v$$

where $m_p$ is mass of the package, $M$ is mass of the boat, $m$ is mass of the child, $u$ is speed of the boat after collision.

$$u = \frac {1 0 \frac {m}{s} \cdot 5 . 7 5}{2 3 . 6 + 3 7 . 6} = - 0. 9 3 \frac {m}{s}$$

Sign “-” means boat’s velocity directed opposite to package’s velocity.

Answer: 0.93 m/s

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