b) Give the gravitationalptal energy associated with the child and her kinetic e

Question

b) Give the gravitationalptal 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 wing as necessary: height h, mass m, and gravitational acceleration g.) potential energy kinetic energy top of the waterslide mgh launching point mglth/8) in the pool (c) Determine her initial speed vo 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, vox Ymaxmg (e) Use the x-component of the answer to part (c) to eliminate vo from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle . ymax = (f) Would your answers be the same if the waterslide were not frictionless? Yes No

Explanation / Answer

D) eneggy conservation at Ymax height. At this point child will only have X component of velocity.

So (1/2)*m*vox² = m*g*(h - ymax) => (1/2)*vox² = g*(h - ymax) =>vox² / (2g) = (h - ymax)

=> ymax = h – (vox²/(2g)) Answer

E) x-component of vo is vo cos = { [1.6 g h] } * cos

vox = vo cos = ( (1.6*g*h)) * cos

ymax = h – (vox²/(2*g)) = h - (1.6*g*h*(cos )²) / (2*g) Answer

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