Question

question 8
a 73.6 kg person jumps along a dock at 5.92 m/s and jumps into a 700 kg rowboat. what is the final velocity of the boat and its new occupant as they drift away from the dock?
1 point
question 9
a 55 kg girl sits wearing a pair of roller skates stands still while holding a 16.6 kg bucket. if she throws the bucket away from her at 3.14 m/s, what is her resulting velocity?
1 point
3 of 10 questions remaining

Explanation:

Step1: Identify the principle

Use the law of conservation of momentum $p = mv$, where $p$ is momentum, $m$ is mass and $v$ is velocity. Initial momentum is zero (system at rest).

Step2: Set up equation for Question 8

Let $m_1 = 73.6$ kg (mass of person), $v_1=5.92$ m/s (velocity of person), $m_2 = 700$ kg (mass of boat). According to conservation of momentum $m_1v_1+m_2v_2 = 0$. Solve for $v_2$ (velocity of boat).
$v_2=-\frac{m_1v_1}{m_2}$
$v_2 =-\frac{73.6\times5.92}{700}$
$v_2=-\frac{435.712}{700}\approx - 0.622$ m/s

Step3: Set up equation for Question 9

Let $m_{girl}=55$ kg, $m_{bucket}=16.6$ kg, $v_{bucket}=3.14$ m/s. According to conservation of momentum $m_{girl}v_{girl}+m_{bucket}v_{bucket}=0$. Solve for $v_{girl}$ (velocity of girl).
$v_{girl}=-\frac{m_{bucket}v_{bucket}}{m_{girl}}$
$v_{girl}=-\frac{16.6\times3.14}{55}$
$v_{girl}=-\frac{51.924}{55}\approx - 0.944$ m/s

Answer:

Question 8: The final velocity of the boat is approximately $- 0.622$ m/s.
Question 9: The resulting velocity of the girl is approximately $- 0.944$ m/s.