Rebecca of mass 50 kg and Robert of mass 60 kg are initially at rest on a frictionless frozen lake.Robert throws a book of mass 0.50 kg at Rebecca with 20 m/s relative to the ice.Rebecca catches the book.Assuming the book is traveling horizontally,their final speeds are A)V_Reb = 12.0 m/s,V_Rob = 17.0 m/s. B)V_Reb = 1.51 m/s,V_Rob = 4.17 m/s. C)V_Reb = 0.20 m/s,V_Rob = 0.17 m/s. D)V_Reb = 0.12 m/s,V_Rob = 6.17 m/s.

Question

Quizplus · Accepted Answer

Since the system is initially at rest and isolated, momentum is conserved. The total momentum before the book is thrown is zero, and it must remain zero after the book is thrown and caught. Let $v_{\text{Reb}}$ be Rebecca's final speed and $v_{\text{Rob}}$ be Robert's final speed. The book's mass is $m_{\text{book}} = 0.50 \, \text{kg}$, Rebecca's mass is $m_{\text{Reb}} = 50 \, \text{kg}$, and Robert's mass is $m_{\text{Rob}} = 60 \, \text{kg}$. The speed of the book relative to the ice is $v_{\text{book}} = 20 \, \text{m/s}$.For Robert to throw the book at $20 \, \text{m/s}$ relative to the ice, he and the book must move in opposite directions to conserve momentum. The momentum of the book is $m_{\text{book}} \cdot v_{\text{book}}$, and the momentum of Robert and Rebecca must be equal and opposite to this.After catching the book, Rebecca's momentum is $(m_{\text{Reb}} + m_{\text{book}}) \cdot v_{\text{Reb}}$, and Robert's momentum is $m_{\text{Rob}} \cdot v_{\text{Rob}}$. Setting the total momentum before and after the throw to be equal and solving for $v_{\text{Reb}}$ and $v_{\text{Rob}}$ gives the correct speeds that match the conservation of momentum principle.

Rebecca of Mass 50 Kg and Robert of Mass 60