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WIN11
Phys 2A
Assignment 2.19
2.19 For a spherical celestial object of radius R, the acceleration due to grav
ity g at a distance x from the center of the object is
g
=
g
0
R
2
/x
2
, where
g
0
is the
acceleration due to gravity at the object’s surface and
x > R
. For the moon, take
g
0
= 1
.
63 m/s
2
and
R
= 3200 km. If a rock is released from rest at a height of 5
R
above the lunar surface, with what speed does the rock impact the moon?
Hint: Its
acceleration is a function of position and increases as the object falls. So do not use
constant acceleration freefall equations, but go back to basics.
WARNING: the value given for the initial height may be di±erent for your assign
ment.
CAUTION: The problem is missworded. Instead of “If a rock is released from rest
at a height of
nR
above the lunar surface, with what speed .
. . ” it should say “If a
rock is released from rest at a distance of
nR
from the lunar center, with what speed
. . . ” where
n
is an integer that however may be di±erent for di±erent students.
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 Spring '09
 SHARMA

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