Two people,each ofmass m,stand atopposite ends ofawheeled platform of mass M and of length Las shown in Fig. 9.13.1.0ne person holds a medicine ball of mass m. . Initially, the people and the platform are at rest relative to the ground. The person at the right end ofthe 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 ex; note that 0,, 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. iii*- mass m +r Medicine ball ms :1: 1 +1" mass M Interactive Figure 9.13.1: Two exercise enthusiasts are tossing a medicine ball between them on a wheeled platform. Keyldeas: This problem is rich with interesting phvsics, so let's make a list of important ideas to consider. 3 Let's choose the system to consist ofthetwo people, the platform, and the medicine ball. o Is there a net, external force on this system during the motion? The answer should not be given too quickly. When either one ofthe two people is holdingthe medicine ball, the answer is simple: no. What about when the ball is in ight while travelingfrom 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 answerthe question as follows: Fneixxfm : U ' Fm'i'mxi.) # 0 _) } The vector relationship F "m.\" = d P 1dr allows us to conclude that the x component of the total linear momentum does not change, but the ycomponent does change. In other words, the key physics concept guiding our solution is as follows: API = 0 Let's apply this concept to two different instantsrst, an instant sometime before the medicine ball is thrown [as depicted in Fig. 9.13.1}, and second,just afterthe person on the right side of the platform releases the ball. This second instant is depicted in Fig. 9.13.2. L Medicine ball +1 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 of the platform. The ball is shown with an initial velocity 3'0, and them.' component of the initial velocity is also shown. In order to conserve the 1* component of the system's linear momentum. the platform recoils in the opposite direction with a _} velocity thatis labeled V . Question 1 What is the recoil velocity Vof the platform while the ball is in the air? This will be a symbolic expression in terms of M', m' m1, and 2:3. mm Save for L: 5' Attempts: 0 of 2 used Question 2 What is the time interval At in which the platform is in motion? This will be a symbolic expression in terms of L M, m, 177.], and lvzl (note the absolute value). At 2D Ssh-e for Late Attempts: 0 of 2 used Question 3 What is the total distance traveled by the platform?This will be a symbolic expression in terms of M. m, m1, and L. D=m Save for Lste , Attempts: 0 of 2 used