A 130 kg rocket is moving radially outward from the earth at an altitude of 190

Question

A 130 kg rocket is moving radially outward from the earth at an altitude of 190 km above the surface with a velocity of 3.9 km/sec. At this point, its final stage engine shuts off.

1)

Ignoring any minor air resistance, what is the rocket's velocity 990 km above the surface of the earth?";

m/sec

Your submissions:

1400

Correct!

2)

Again ignoring any minor air resistance, what is the rocket's velocity 990 km above the surface of the earth if its mass were 260 kg?

m/sec

Your submissions:

1400

Correct!

3)

What is the maximum height of the rocket above the earth's surface (using the initial rocket mass )

m

Your submissions:

385000

incorrect

Could someone please help me with number 3?? Thank you in advance!

PS: The answer is not 2.85 X 10 ^5 m

Explanation / Answer

at 190 km point

KE1 = 0.5*m*v1^2 = 0.5*130*3900^2 = 9.88*10^8 J

PE1 = -G*M*m/(R+h)

PE1 = -((6.67*10^-11*5.97*10^24*130)/(6.37*10^6+190000))

PE1 = -7.89*10^9 J

total energy of the rocket at 190 km = TE1 = -6.9*10^9 J

at the maximim height H the rocket has only PE

PE2 = -G*Mm/(R+H)

PE2 = -((6.67*10^-11*5.97*10^24*130)/(6.37*10^6+H)

PE2 = -5.27*10^16 / (6.37*10^6+H)

KE2 = 0

total energy at maximum height TE2 = -5.17*10^16 / (6.37*10^6+H)

from energy conservation

TE2 = TE1

-5.17*10^16 / (6.37*10^6+H) = -6.9*10^9

7502300 = (6.37*10^6+H)

H = 11.32*10^5 m <-----answer

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