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Man jumping into water: Conservation of Energy

  1. Dec 13, 2016 #1

    1. The problem statement, all variables and given/known data
    sportsman jumps at 5m/s velocity from 5m cliff to water. at what speed does he reach water?
    so
    given answer is 11.1m/s though in this book there are some wrong answers
    (I did try other equations and I got right answer but I want to know why I can't get it using this one)
    ##g=-10m/s^2##
    ##v_0=-5m/s##
    ##h_0=0m##
    h=-5m

    2. Relevant equations

    I'm trying to do this using ##E_k1 + E_p1 = E_k2 + E_p2##
    ##E_k=\frac {mv^2}{2}##
    ##E_p=mgh=\frac {2mgh}{2}##

    3. The attempt at a solution
    since ##h_0=0## ##E_p1=0##

    putting in values

    ##\frac {mv_0^2}{2}=\frac {mv^2}{2}+\frac {2mgh}{2}##

    after multiplying everything by 2 and dividing by m
    ##v_0^2=v^2+2gh##

    ##v^2=v_0^2-2gh##

    ##h=h_1-h_0##
    ##v^2=(-5)^2-2*(-10)*(-5-0)=25-100=-75##
    v=root from -75=impossible. and root from 75 is wrong answer.

    if I used one positive number in -2gh part I will get right answer. I think I might need to use |h| in these kind of formulas?​
     
  2. jcsd
  3. Dec 13, 2016 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    In the potential energy formula mgh, g represents the magnitude of the acceleration of gravity. So, g is a positive quantity.
     
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