19. REASONING During the breakup¸ the linear momentum of the system is conserved, since the force causing the breakup is an internal force. We will assume that the +x axis is along the original line of motion (before the breakup), and the +y axis is perpendicular to this line and points upward. We will apply the conservation of linear momentum twice, once for the momentum components along the x axis and again for the momentum components along the y axis.
SOLUTION The mass of each piece of the rocket after breakup is m, and so the mass of the rocket before breakup is 2m. Applying the conservation of momentum theorem along the original line of motion (the x axis) gives
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(1)
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Applying the conservation of momentum along the y axis gives
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(2)
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a. To find the speed v1 of the first piece, we substitute the value for v2 from Equation (2) into Equation (1). The result is
Solving for v1 and setting v0 = 45.0 m/s yields
b. The speed v2 of the second piece can be found by substituting v1 = 77.9 m/s into Equation (2):
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