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In Example 8.14 (Section $8.5 ),$ Ramon pulls on the rope to give himself a speed of 0.70 $\mathrm{m} / \mathrm{s}$ . What is James's speed?

$v_{J}=0.47\mathrm{m/s}$

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in this question to friends. James and Ramon are playing tug of war. Ramon has a mass off 60 kg and James has a mass off 90 kg. At some point in time, Ramon suddenly pulls the rope and achieves a speed off 0.7 m per second to the left. By the principle of conservation of momentum, we expect that James will also move with some speed to the right. In this question, we have to calculate what is the speed that James achieve. For that, we're going to use the principle of conservation of momentum. That principle tells us that the net momentum is conserved in any kind of situation where no external forces are acting on our system, which is just our case. So applying the principle of conservation of momentum, we have the following the momentum before the pool is equal to the momentum. After the pool. Let me use these reference frame where everything that points the right is positive. Then in this reference frame, we have the following. Before there was no one moving, so the net momentum before is equals to zero after the pool, both off them are moving James with a mass off 90 kg is moving to the right the positive direction off a reference frame with velocity V. At the same time, Ramon, with a mass off 60 kg, is moving to the left with a velocity off 0.7 m per second. It has a negative sign because it points to the negative direction off our reference frame. Now all we have to do is solve this equation for V. We do that as follows. We begin by sending this term toe the left hand side. So we have 60 times 0.7 is equal to 19 times V. Then we send 90 to the other side dividing. So we have V is equals to 60 times 0.7, divided by 90 by Soviets calculation. We get a velocity off approximately 0.47 m per second to the right and this is the answer to this question.

Brazilian Center for Research in Physics