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.
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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