A child of mass m starts from rest and slides withoutfriction from a height h along a

Chapter 8, Problem 27

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A child of mass m starts from rest and slides withoutfriction from a height h along a slide next to a pool(Fig. P8.27). She is launched from a height h/5 intothe air over the pool. We wish to find the maximumheight she reaches above the water in her projectilemotion. (a) Is the childEarth system isolated or nonisolated? Why? (b) Is there a nonconservativeforce acting within the system? (c) Define the configurationof the system when the child is at the waterlevel as having zero gravitational potential energy.Express the total energy of the system when the childis at the top of the waterslide. (d) Express the totalenergy of the system when the child is at the launchingpoint. (e) Express the total energy of the systemwhen the child is at the highest point in her projectilemotion. (f) From parts (c) and (d), determine her initialspeed vi at the launch point in terms of g and h.(g) From parts (d), (e), and (f), determine her maximumairborne height ymax in terms of h and the launchangle u. (h) Would your answers be the same if thewaterslide were not frictionless? Explain.