Question

If a man jumps out from a boat, the boat moves backward. Explain.

Answer 1

Hint Firstly, we will write down Newton's third law and Newton’s second law. We also know that the conservation of linear momentum. So, we will first calculate the initial momentum when (boatman) system is at rest. The linear momentum will be zero. Then we will calculate the velocity of the boat when the man jumps out from a boat. Due to conservation of linear momentum we will see that the boat will start moving backwards.

Complete step by step solution
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the man jumps from a boat, he applies force on the boat due to which boat moves backward. An equal force is exerted by the boat on the man which helps the man to jump out of the boat.
Again, Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the applied force. Hence in the absence of external force there is no change in linear momentum
Initially both the passenger and the boat are stationary and have a total mass ${m_1} + {m_2}$ but total velocity will be zero. So, they have zero momentum.
When the passenger jumps out from a boat.
Let the velocity of the person becomes ${v_1}$
So, the linear momentum becomes ${m_1}{v_1}$
The total linear momentum is conserved so let the boat should have a momentum ${m_2}{v_2}$
Initial momentum should be equal to the final momentum according to the conservation of linear momentum.
 ${m_1}{v_1} + {m_2}{v_2} = 0$
 $\therefore {v_2} = - \dfrac{{{m_1}}}{{{m_2}}}{v_1}$
The negative sign indicates that the boat moves in a backward direction.

Note In the absence of any external force acting on a system of bodies even if interactions exist among the bodies, the total linear momentum of the system remains constant. This incident can also be explained in terms of action- reaction force. When the man steps out, he pushes the boat with his foot in the backward direction. The push on the boat is called action. The boat exerts an equal force in the forward direction which helps him to move forward. The force exerted by the boat is called reaction. So due to this reaction force the boat moves backward due to the force exerted by the man. So that’s why if a man jumps out from a boat, the boat moves backward.