Solved: A child of mass m starts from rest and slides

Chapter 5, Problem 5.3.46

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A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (c) Determine her initial speed v0 at the launch point in terms of g and h. (d) Determine her maximum airborne height ymax in terms of h, g, and the horizontal speed at that height, v0x. (e) Use the x-component of the answer to part (c) to eliminate v0 from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle u. (f) Would your answers be the same if the waterslide were not frictionless? Explain.