# Homework Help: Energy Conservation applied to Earth's surface

1. Nov 9, 2014

### garr6120

1. The problem statement, all variables and given/known data
With what initial speed must an object be projected vertically upward from the surface of Earshot rise to a maximum height equal to Earth's radius? (neglect air resistance.) Apply energy conservation.

2. Relevant equations
$E_{k_1}+E_{g_1}=E_{k_2}+E_{g_2}$, however since $E_{g_1}=0$ and $E_{k_2}=0$,
the equation is $E_{k_1}=E_{g_2}$.
$E_{k_1}=\frac{mv^2}2$
$E_{g_2}=mgh$

3. The attempt at a solution
$\frac{mv^2}2=mgh$
$v=\sqrt{2gh}$
I know that the maximum height of the object is $6.38*10^6 m$
I do not know if this is the right formula that i am using because i get the wrong answer.
The answer is supposed to be 7.91*10^3 m/s.

2. Nov 9, 2014

### Staff: Mentor

mgh for gravitational PE only applies to bodies close to the surface of the Earth. Since this problem involves a distance that is double the Earth's radius you should revert to Newton's general formula.

3. Jan 23, 2018

### susu

LCE: Ek1= Eg2
mv^2/2 = -Gmem/re + alt
Where m=mass of the object and
me=mass of the earth
Alt= distance above Earth's surface

You'll see that m cancels out so ur left with

V^2 = -Gme/re + re
U rearrange to get
V= √ 2Gme/2 re