A 160 kg rocket is moving radially outward from the earth at an altitude of 210

Question

A 160 kg rocket is moving radially outward from the earth at an altitude of 210 km above the surface with a velocity of 3.8 km/sec. At this point, its final stage engine shuts off.

1)

Ignoring any minor air resistance, what is the rocket's velocity 960 km above the surface of the earth?";

2)

Again ignoring any minor air resistance, what is the rocket's velocity 960 km above the surface of the earth if its mass were 320 kg?

3)

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

Explanation / Answer

conserving the energy,

G Mm/r1 + 1/2 mv1^2 = -GMm/r2 + 1/2mv2^2

here,

M= 6*10^24 kg, r1 = 6400+210 = 6610 km, r2 = 6400+960 = 7360

v1 = 3800 m/s, we need to calculate v2,

knowing all other things, we can easily

calculate v2.

2] if m = 320 ,

we can see that, m cancel's out of the equation,

so , velocity does nt depend on the mass (if air friction is neglected)

3] for calculating maximium height,

v2 (final velocity must be zero)

so we'll put v2 as 0 in above equation ,

that 'll give us r2.

max height will be = (r2- 6400) km

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