# Escape Speed problem

Hi friends.

Somewhere in a reference book I read about escape speed of a particle for earth.
Let a particle is projected from the earth surface. Let its mass be m and speed of projection be u. Let mass of earth be M and its radius be R.

According to law of conservation of energy,
https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-prn2/q86/s720x720/1175485_1407193806174392_209657781_n.jpg
https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn2/q88/s720x720/1236159_1407193812841058_1152852378_n.jpg
The problem is that,

If the Ist term becomes negative also but its magnitude is less than the IInd term, then also final Kinetic energy will be positive. And the particle will never doesn't give the proper answer. Friend isn't it so?

Simon Bridge
Homework Helper
The first term in what? You mean term I in the first relation?
That's kinetic energy - does it make physical sense to have a negative kinetic energy?

The first term in what? You mean term I in the first relation?
That's kinetic energy - does it make physical sense to have a negative kinetic energy?
The first term is in the second relation. the complete 1/2(mu2) - (GMm)R

The complete term can be negative due to less value of 1/2 (mu2).

Bandersnatch
This means that the second term $\frac{GMm}{R+h}$ will always be zero. So the first term can not be less in magnitude than the second one.