(a) A space vehicle is launched vertically upward from the Earth\'s surface with
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Question
(a) A space vehicle is launched vertically upward from the Earth's surface with an initial speed of 8.55 km/s, which is less than the escape speed of 11.2 km/s. What maximum height does it attain?
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A space vehicle is launched vertically upward from the Earth's surface with an initial speed of 8.55 km/s, which is less than the escape speed of 11.2 km/s. What maximum height does it attain? A meteoroid falls toward the Earth. It is essentially at rest with respect to the Earth when it is at a height of 2.54 times 107 m above the Earth's surface. With what speed does the meteorite (a meteoroid that survives to impact the Earth's surface) strike the Earth?Explanation / Answer
using conservation of energy.
1/2mv*v - GmM/R = 0 - GmM / X.------------------------------(1)
final kinetic energy is zero.
initial velocity is v = 8.55 Km/s.
at escape velocity 1/2 mve*ve = GmM/R.
at 8.55
we get 1/2mv*v = a * [ 1/2 mve*ve ] = a* [ GmM/R ]
a= 8.55*8.55 / [11.2*11.2]
= 0.5827.
from (1)
[0.5827 -1] *GmM/R = - GmM/X.
0.417*X = R
X = 6371000 / 0.417
= 15269706 m
= 15269.7 Km.
height reached = 15269.7 - 6371 = 8898 Km.
b)
from conservation of energy
intial kinetic energy is zero
so
0 - GmM/X = 1/2m*v*v - GmM/R.
GM/X = 1/2*v*v - GM/R
[6.673*10^-11]*[5.97*10^24] [(1/6371000) - (1/31771000) ] = 0.5*v*v.
v = 9999.08 m/s
= 9.99908 Km/s.
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