write the equation conservation of momentum
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Momentum is conserved, so we know that at all times p c + p b = 0 \mathbf{p}_\mathrm{c} + \mathbf{p}_\mathrm{b} = 0 pc+pb=0p, start subscript, c, end subscript, plus, p, start subscript, b, end subscript, equals, 0. In this case, all the motion is horizontal, so we can use a scalar quantity for the velocity
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