Question

the figure below shows a man in a boat on a lake. the mans mass is 74 kg, and the boats is 124 kg. the man and boat are initially at rest when the man throws a package of mass m = 15 kg horizontally to the right with a speed of v_j = 4.7 m/s. what is the velocity of the boat after the package is thrown? neglect any resistance force from the water. (give the magnitude in m/s, and select the correct direction from the options given.)

Explanation:

Step1: Apply the law of conservation of momentum

The initial momentum of the system (man + boat + package) is \(P_{i}=0\) (since they are initially at rest).
According to the law of conservation of momentum \(P_{i} = P_{f}\), where \(P_{f}=m_{package}v_{j}+(m_{man}+m_{boat})v\)

Step2: Solve for the velocity of the boat \(v\)

We know \(P_{i} = P_{f}\), so \(0=m_{package}v_{j}+(m_{man}+m_{boat})v\)

$$
LATEXBLOCK0
$$

Substitute \(m_{package} = 15\space kg\), \(v_{j}=4.7\space m/s\), \(m_{man}=74\space kg\) and \(m_{boat}=124\space kg\)

$$
LATEXBLOCK1
$$

Answer:

The magnitude of the velocity is \(0.36\space m/s\) and the direction is to the left.