# A Rocket's Distance from the center of the moon

• gc33550

## Homework Statement

The Moon has a mass of M= 7.0E22 kg and a radius of R=1.75E6 m. A projectile with
mass m=10 kg is shot straight up from the Moon’s surface with an initial speed of 500 m/s. What is the maximum distance from the center of the Moon that this projectile can reach?

## Homework Equations

E_initial=E_final
Kinetic_initial=Grav_potential
.5mv^2=GMm/r

## The Attempt at a Solution

Thinking through this I believe this is wrong, because essentially that is the equation for escape velocity. We don't know for sure that this rocket will escape... I am lost...

Thinking through this I believe this is wrong, because essentially that is the equation for escape velocity. We don't know for sure that this rocket will escape... I am lost...

It is true for any velocity. Calculate r.

I didn't get the right answer...

r=(2GM)/v^2 is what i believe I worked it out to so

r=(2*6.7E-11*7E20)/500^2

r=3.752E5

According to the answer key it is supposed to be 1.84E6

So is there something I am missing I thought a simple energy conservation would cover it

Use the equation :

K+U = K_o+U_o

where K could be 1/2mv^2
and U = -GMm/r

Use the equation :

K+U = K_o+U_o

where K could be 1/2mv^2
and U = -GMm/r

I am assuming that there is no kinetic in my final state because the rocket doesn't have enough velocity to escape according to sqrt(2GM/r) so then:

(GMm/r_final)=.5mv^2+GMm/r_initial

r=GMm/(.5mv^2+(GMm/r_initial))

r= 6.7E-11*7E22*10/(.5*10*500^2+((6.7E-11*7E22*10)/1.75E6))

r=1.672e6
I still don't get the correct answer

here :

-GMm/ r =1/2m*v^2 - GMm/R_e

r = (1/R_e - v^2 / (2*G*M_e ) ^-1

r = 1.84E^6

Could I get a short explanation on that? I don't follow your variables

Could I get a short explanation on that? I don't follow your variables

r=(-2*M_e*G*R_e)/(v^2*R_e-2*G*M_e)

r=(-2*7e22*6.7e-11*1.75e6)?(500^2*1.75e6-2*6.7e-11*7e22)

r=1.84e6

Good luck with your test today, I've been up all night studying for it, hope this helps!

Maybe my brain is physics fried haha But which Variables need to be negative and why? Is it both potentials? I thought the would have positive potential energy or is it the fact that it is in the negative direction? Oh boy I am going to fail haha

Use the equation :

K+U = K_o+U_o

where K could be 1/2mv^2
and U = -GMm/r

Use exactly what tnutty has written here for positive and negative values.

Dont worry about the final, I don't know if anyone is going to do well on it, its bad if I am aiming for a 50% on it...

But which Variables need to be negative and why? Is it both potentials? I thought the would have positive potential energy or is it the fact that it is in the negative direction?
The gravitational potential expression is

PE = -GM/r

So for your problem they would both carry a negative sign.

I also have my final today. Your's not with jones is it?

Jones? I go to Purdue

By the way I got it thanks guys... Those negative signs will get you every time haha

NO problem