A 140 kg rocket is moving radially outward from the earth at an altitude of 220

Question

A 140 kg rocket is moving radially outward from the earth at an altitude of 220 km above the surface with a velocity of 3.5 km/sec. At this point, its final stage engine shuts off.

1)

Ignoring any minor air resistance, what is the rocket's velocity 830 km above the surface of the earth?";

2)

Again ignoring any minor air resistance, what is the rocket's velocity 830 km above the surface of the earth if its mass were 280 kg?

3)

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

Thank you.

Explanation / Answer

1) TE 1 = 0.5*m*u^2 - GMm/r1

TE2 = 0.5*m*v^2 - GMm/r2

TE2 = TE1

0.5*m*v^2 - GMm/r2 = 0.5*m*u^2 - GMm/r1

0.5*(v^2 -u^2) = GM*((1/r2)-(1/r12))

0.5*(v^2 - 3500^2)= (6.67*10^-11*5.97*10^24)*((1/(6400000+830000))-(1/(6400000+220000)))

v = 1.49 km /s

2) v = 1.49 km /s

3) at max height.......v = 0

TE3 = -GMm/r3 = -GMm/(R+h3)

TE3= TE1

GMm/(R+h3)= 0.5*m*u^2 - GMm/r1

-GM/(R+h3) = (0.5*3500^2)-((6.67*10^-11*5.97*10^24)/(6400000+220000))

h3 = 970519.57 km

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