Calculate the vertical motion of a piece of debris from an explosion

[starstruck_]

< Mentor Note -- thread moved to HH from the technical physics forums (because of a forum issue), so no HH Template is shown >[/color]

There was a huge explosion, one small piece of debris was launched upward at v=5.3 km/s. Calculate its maximum altitude.

a) Develop an expression for the maximum altitude assuming the change in potential energy = mgh
b) derive an algebraic expression for the maximum altitude using U= -GMm/r.

For a) I set 1/2mv^2 = mgh, therefore
h= v^2/(2g)

I’m not exactly sure how to work with b.
I wasn’t there for this lecture. This is what I’m assuming and I’m most likely understanding this incorrectly. -GMm/r would be equal to the change in potential energy I guess? Which would be 0- 1/2mv^ = -1/2mv^2? I set that equal to -GMm/r? I’m not completely sure.

 

[scottdave]

You have a U0 (potental energy at launch point), then a Ufinal (potential energy at the peak. You need to find the difference between those.

 

[starstruck_]

You have a U0 (potental energy at launch point), then a Ufinal (potential energy at the peak. You need to find the difference between those.

From what I’m understanding :

Etotal 1= E total2

1/2mv^2 - GMm/r (potential energy assuming it is on the surface when it explodes)

= 0- GMm/r+h where h is its altitude above the surface of the Earth ?

 

[haruspex]

From what I’m understanding :

Etotal 1= E total2

1/2mv^2 - GMm/r (potential energy assuming it is on the surface when it explodes)

= 0- GMm/r+h where h is its altitude above the surface of the Earth ?

If you mean 0- GMm/(r+h), yes.