Question

An instrument package is projected vertically upward to collect data near the top of the Earth's...

An instrument package is projected vertically upward to collect data near the top of the Earth's atmosphere (at an altitude of about 840 km ).

Part A

What initial speed is required at the Earth's surface for the package to reach this height?

Express your answer using two significant figures.

Part B

What percentage of the escape speed is this initial speed?

Express your answer using two significant figures.

Homework Answers

Answer #1

part A

at earth surface, total energy = P.E. + K.E.

= -GMm/R + mvi2/2

at the top of earth’s atmosphere, total energy = P.E. + K.E.

= -GMm/(R+h) + mvf2/2

as per energy conservation,

-GMm/R + mvi2/2 = -GMm/(R+h) + mvf2/2

As per given conditions

-GMm/R + mvi2/2 = -GMm/(R+h) + 0 (as vf =0)

-GM/R + vi2/2 = -GM/(R+h)

vi2 = 2GM{1/R - 1/(R+h)} = 79.666x1013(1.813x10-8) = 144.434x105

vi = 3800.447 m/s

and as per required format, the answer is vi = 3800 m/s.

part B

as escape speed = 11200 m/s.

hence the above mentioned speed is (3800/11200)(100)=33.93 % of escape speed.

and as per required format, the answer 34%.

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