How does gravitational variation affect kinetic energy calculations?

[d4nk1337sauce]

Homework Statement

A 1600 kg object is initially at rest 400 km above the earth’s surface. The object falls straight
down and generates 8.3
x10^8J of heat energy while descending to an altitude of 100 km.

Homework Equations

KE+PE+HEAT=KE+PE+HEAT

The Attempt at a Solution

i made PE at 100km above Earth and got 1600x9.81x300000=800V^2+8.3x10^2J
i got V=2200 but the answer should be 2100 about last 2 digits can be off by a bit I am not sure where i go wrong

 

[cupid.callin]

Homework Statement

A 1600 kg object is initially at rest 400 km above the earth’s surface. The object falls straight
down and generates 8.3
x10^8J of heat energy while descending to an altitude of 100 km.

Homework Equations

KE+PE+HEAT=KE+PE+HEAT

The Attempt at a Solution

i made PE at 100km above Earth and got 1600x9.81x300000=800V^2+8.3x10^2J
i got V=2200 but the answer should be 2100 about last 2 digits can be off by a bit I am not sure where i go wrong

What do we need to find here ?
What is V? velocity?

 

[LawrenceC]

Hint: Your altitude is lofty.

 

[d4nk1337sauce]

Hint: Your altitude is lofty.

sorry for the late reply iv been working 8 hours everyday.

even after i made PE at 0km and subtracted mgh100km from 400km i got 2200 I am not sure what you mean any more hits? please lol?

honestly i guess i don't really know what lofty means haha

 

[d4nk1337sauce]

What do we need to find here ?
What is V? velocity?

velocity yes sorry for late response iv have been working quite a bit

 

[cjl]

sorry for the late reply iv been working 8 hours everyday.

even after i made PE at 0km and subtracted mgh100km from 400km i got 2200 I am not sure what you mean any more hits? please lol?

honestly i guess i don't really know what lofty means haha

Hint: PE = mgh assumes gravity is constant. When you're talking about altitudes in the hundreds of kilometers, you can't necessarily make that assumption any more. Do you know any formulas for potential energy that don't assume constant gravity?

 

[d4nk1337sauce]

Hint: PE = mgh assumes gravity is constant. When you're talking about altitudes in the hundreds of kilometers, you can't necessarily make that assumption any more. Do you know any formulas for potential energy that don't assume constant gravity?

yeah i got it i was kinda suprised they would make us us m1m2G/r and i found out what lofty ment lol thanks for the help