Answer
(a) The mass of the particle at the origin is 0.30 kg.
(b) $p = 2.0~kg~m/s$
(c) The velocity of the particle at the origin is 6.67 m/s.
Work Step by Step
(a) $x_{cm} = \frac{m_1x_1+m_2x_2}{m_1+m_2}$
$x_{cm}~(m_1+m_2) = m_1~(0)+m_2x_2$
$m_1 = \frac{m_2x_2 - m_2x_{cm}}{x_{cm}}$
$m_1 = \frac{(0.10~kg)(8.0~m) - (0.10~kg)(2.0~m)}{2.0~m}$
$m_1 = 0.30~kg$
The mass of the particle at the origin is 0.30 kg.
(b) $p = m~v_{cm}$
$p = (0.40~kg)(5.0~m/s)$
$p = 2.0~kg~m/s$
(c) $m_1v_1 + m_2~v_2 = p$
$m_1v_1 + 0 = p$
$v_1 = \frac{p}{m_1} = \frac{2.0~kg~m/s}{0.30~kg}$
$v_1 = 6.67~m/s$
The velocity of the particle at the origin is 6.67 m/s.
