Two people, each of mass m, stand at opposite ends of a wheeled platform of mass M and oflength I as shown in Fig. 9.13.1. One person holds a medicine ball of mass m₁. Initially, thepeople and the platform are at rest relative to the ground. The person at the right end of theplatform then tosses the medicine ball with some initial velocity toward the other person whocatches the ball. While in flight, the constant x velocity of the medicine ball is ux; note thatUx is a negative number. Our goal is to find how far, and in what direction, the platform travelswhile the medicine ball is in flight.mass MInteractive Figure 9.13.1: Two exercise enthusiasts are tossing a medicine ball betweenthem on a wheeled platform.Key Ideas: This problem is rich with interesting physics, so let's make a list of important ideas toconsider.Question 1• Let's choose the system to consist of the two people, the platform, and the medicine ball.• Is there a net, external force on this system during the motion? The answer should not begiven too quickly. When either one of the two people is holding the medicine ball, the answer issimple: no. What about when the ball is in flight while traveling from one person to the other?The force due to gravity on the ball is not balanced by any other force, so now the answer is:yes. Of course, the force due to gravity acts vertically downward, which is in the - y direction.It is true, however, that there are no external horizontal forces. So we can answer the questionas follows:VLet's apply this concept to two different instants-first, an instant sometime before themedicine ball is thrown (as depicted in Fig. 9.13.1), and second, just after the person on theright side of the platform releases the ball. This second instant is depicted in Fig. 9.13.2.LMedicine ballLCorrect!Medicine ballmass miQuestion 2At =m₁ X v₂2m + MRecoil velocityInteractive Figure 9.13.2: An instant is depicted just after the medicine ball is released andbegins traveling toward the person at the other end of the platform. The ball is shown withan initial velocity 70, and the x component of the initial velocity is also shown. In order toconserve the x component of the system's linear momentum, the platform recoils in theopposite direction with a velocity that is labeledDFnet,ext, x = 0, Fnet,ext,y # 0mass mWhat is the recoil velocity V of the platform while the ball is in the air? This will be a symbolicexpression in terms of M, m, m₁, and v.L(M+2m)|vx|(M+ m₂)Question 3Ux+y+XWhat is the time interval At in which the platform is in motion? This will be a symbolicexpression in terms of L, M, m, m₁, and v(note the absolute value).+XDid you use the fact that the platform travels with constant velocity VV andthat the distance between the two people standing on the platform is LL? Howfast is the medicine ball traveling relative to the second person who is going tocatch it?What is the total distance traveled by the platform? This will be a symbolic expression interms of M, m, m₁, and L.

Mass of person=mMass of platform=MInitial velocity of the ball=vo→ with vx negative

Two people, each of mass m, stand at opposite ends of a wheeled platform of mass M and of length I as shown in Fig. 9.13.1. One person holds a medicine ball of mass m₁. Initially, the people and the platform are at rest relative to the ground. The person at the right end of the platform then tosses the medicine ball with some initial velocity toward the other person who catches the ball. While in flight, the constant x velocity of the medicine ball is ux; note that Ux is a negative number. Our goal is to find how far, and in what direction, the platform travels while the medicine ball is in flight. L mass M Interactive Figure 9.13.1: Two exercise enthusiasts are tossing a medicine ball between them on a wheeled platform. Medicine ball mass mi Question 1 Key Ideas: This problem is rich with interesting physics, so let's make a list of important ideas to consider. • Let's choose the system to consist of the two people, the platform, and the medicine ball. • Is there a net, external force on this system during the motion? The answer should not be given too quickly. When either one of the two people is holding the medicine ball, the answer is simple: no. What about when the ball is in flight while traveling from one person to the other? The force due to gravity on the ball is not balanced by any other force, so now the answer is: yes. Of course, the force due to gravity acts vertically downward, which is in the - y direction. It is true, however, that there are no external horizontal forces. So we can answer the question as follows: Correct! V = Fnet,ext.x=0, Fnet,exty #0 Let's apply this concept to two different instants-first, an instant sometime before the medicine ball is thrown (as depicted in Fig. 9.13.1), and second, just after the person on the right side of the platform releases the ball. This second instant is depicted in Fig. 9.13.2. L Medicine ball m₁ X v₂ 2m + M mass m +y ก Ux +X +X V Recoil velocity Interactive Figure 9.13.2: An instant is depicted just after the medicine ball is released and begins traveling toward the person at the other end the platform. The ball is shown with an initial velocity 70, and the x component initial velocity is also shown. In order conserve the x component of the system's linear momentum, the platform recoils in the opposite direction with a velocity that is labeled V. What is the recoil velocity V of the platform while the ball is in the air? This will be a symbolic expression in terms of M, m, m₁, and v.