http://www.webassign.net/serpse8/8-p-027.gif A child of mass m starts from rest
ID: 2195930 • Letter: H
Question
http://www.webassign.net/serpse8/8-p-027.gif
A child of massmstarts from rest and slides without friction from a heighthalong a slide next to a pool (see figure). She is launched from a heighth/5 into the air over the pool. We wish to find the maximum height she reaches above the water in her projectile motion.
determine her maximum airborne height ymax in terms of h and the launch angle ?. (Use any variable or symbol stated above as necessary.)
The answer is h(1-4/5cos(theta)^2) I am not sure how they got that.
Explanation / Answer
The kid starts with total energy TE = GPE = mgh and loses mgh - mgh/5 = 1/2 mU^2 = KE. The lost potential energy is 100% converted into kinetic energy at h/5 because there is no friction loss. Total energy at the lip of the slide is TE = 1/2 mU^2 + mgh/5 = KE + pe = mgh = TE Thus U = sqrt(4gh/5) = vi ANS. This is the kid's initial speed off the slide. Max height above h/5 is Y = Uy^2/2g = (U sin(theta))^2/2g = (4gh/5) sin(theta)^2/2g = 4h/10 sin(theta)^2 = (2/5)h sin(theta)^2 ANS.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.