Answer to Question #191151 in Classical Mechanics for Mike

Question

A Stationary lift raft with mass of 160 kg is carrying two survivors with masses of 55 kg and 72 kg, they dive off raft at the same instant the 55 kg person due east at 4.4 m/s and the 72 kg person due north at 4.2 m/s. At what speed and in what direction does the raft start to move?

Answer 1

$\vec{0}=\vec{p_1}+\vec{p_2}+\vec{p},$

$(m_1v_1)^2+(m_2v_2)^2=(Mv)^2,$

$v=\frac{\sqrt{(m_1v_1)^2+(m_2v_2)^2}}{M}=2.42~\frac ms,$

$\alpha=\arctan \frac{m_2v_2}{m_1v_1}=51°$ S of E.