A piece of ejecta is thrown up, what is the velocity

1. Oct 6, 2016

nysnacc

1. The problem statement, all variables and given/known data

2. Relevant equations
energy conservation

3. The attempt at a solution
I used this equation:

1/2 mg R^2/ r1 + 1/2 mv1^2 = 1/2 mg R^2/ r2 + 1/2 mv2^2
For r1, it is 1738 km (radius) + 1000 km (above surface) ?
But for r2 , it is on the surface, so would it be 0??

2. Oct 6, 2016

haruspex

That does not look quite right to me. Are you sure you have quoted it correctly?
Also you need to think about the sign.

3. Oct 6, 2016

nysnacc

Sorry.
mg R^2/ r1 + 1/2 mv1^2 = mg R^2/ r2 + 1/2 mv2^2
For r1, it is 1738 km (radius) + 1000 km (above surface) ?
But for r2 , it is on the surface, so would it be 0??

4. Oct 6, 2016

haruspex

I edited my first reply while you were responding...

5. Oct 6, 2016

nysnacc

So it would be - before mg? based on the definition?

But my concern is mainly what happened with the potiential energe when it hits the surface, cuz the radius above surface will be 0, making the expression 1/0

6. Oct 6, 2016

haruspex

The equations you quote all take radii as being measured from the centre of mass of the moon.

7. Oct 6, 2016

nysnacc

Big R is the radius of the moon
while r is the distance above the surface?

8. Oct 6, 2016

haruspex

You are given the distance above the surface, but the equations you quote require r to be measured from the mass centre of the gravitational body.

9. Oct 7, 2016

nysnacc

V = 1447.98 m/s ??

10. Oct 7, 2016

haruspex

11. Oct 7, 2016

nysnacc

-mg R2/ r1 +1/2 m v12 = -mg R2/r2 +1/2 m v22

r1 is radius + distance above > R , r2 = R

so
-g R2/ r1 +1/2 v12 = -g R +1/2 v22

With v1 = 200 m/s, g = 1.62 m/s2

-2g R2/ r1 + 2g R +v12 = v22

-2g {R2/ r1 - R} + v12 = v22

-2(1.62) (17380002/2738000 - 1738000) + (200)2 = v22

So then v2 is sqrt of the left hand side, = 1447.98 m/s

12. Oct 7, 2016

haruspex

Fair enough... my rough estimate must have had a mistake somewhere. The 200m/s turns out to be insignificant.

13. Oct 7, 2016

nysnacc

But does it make sense to crash the surface at such speed?

14. Oct 7, 2016

haruspex

Quick lower bound: up to 1738km from surface, g is at least 1.6/22=0.4m/s2. Using v2=2as=800,000m2/s2, v is at least 900m/s.