physics energy and work 2

A child of mass m starts from rest and slides without friction from a height h along a curved waterslide. . She is launched from a height h/5 into the pool.

(a) Is mechanical energy conserved?

(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. (Use the following as necessary: height h, mass m, and gravitational acceleration g.) (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 Î¸.

(f) Would your answers be the same if the waterslide were not frictionless?