A stationary satellite in deep space suddenly ruptures into three distinct modules due to an internal failure. The modules have masses M , 2M , and 3M . The module of mass M is ejected along the positive x-axis with a speed of 120 m/s , while the module of mass 2M is ejected along the positive y-axis with a speed of 80 m/s . What is the speed of the heaviest module?

Step-by-step solution

Initial momentum of the satellite is zero. By conservation of linear momentum: P ₁ + P ₂ + P ₃ = 0 The momentum of the first module is P ₁ = M(120 i ) = 120M i . The momentum of the second module is P ₂ = 2M(80 j ) = 160M j . Let the velocity of the heaviest module of mass 3M be v . Its momentum is P ₃ = 3M v . Substituting the values: 120M i + 160M j + 3M v = 0 3M v = -120M i - 160M j v = -40 i - 160 3 j The speed of the heaviest module is the magnitude of its velocity: | v | = (-40)^2 + (- 160 3 )^2 | v | = 1600