Answer:
Step-by-step explanation:
As the three astronauts they push off from each other, their forces are internal. There is no external force so their momenta are conserved and the sum of their momenta are zero.
By conservation of momentum in the y-direction, m_red * vel_y_red + m_blue * vel_y_blue = 0
After 1 sec, red travels 3 units in y-direction while blue travel -3 units in y-direction. So vel_y_red = 3 and vel_y_blue = -3
m_red*3 + m_blue*(-3) = 0
m_red = m_blue
m_red / m_blue = 1
By conservation of momentum in the x-direction, m_green * vel_x_green + m_red * vel_x_red + m_blue * vel_x_blue = 0
After 1 sec, green travels 3 units in x-direction while red travels -2 units and blue travel -4 units in x-direction. So vel_x_green = 3, vel_x_red = -2 and vel_x_blue = -4
m_green*3 + m_red*(-2) + m_blue*(-4) = 0
m_green*3 = m_red*2 + m_blue*4 = m_blue*6
m_green / m_blue = 6/3 = 2
Because there is no external force, the center of mass has not moved after 1 second.