# Man jumping into water: Conservation of Energy

1. Dec 13, 2016

### MrGoATi

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. Dec 13, 2016

### TSny

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