Answer
When the book is on the sled, the sled moves at a speed of $0.83~m/s$
Work Step by Step
By conservation of momentum, the final momentum of the system is equal to the initial momentum. We can find the final speed $v_f$ of the sled after the book is dropped on the sled:
$m_f~v_f = m_0~v_0$
$v_f = \frac{m_0~v_0}{m_f}$
$v_f = \frac{(5.0~kg)(1.0~m/s)}{5.0~kg+1.0~kg}$
$v_f = 0.83~m/s$
When the book is on the sled, the sled moves at a speed of $0.83~m/s$.
