Answer:
5026.55 m/s
Explanation:
Gravitation potential of a body in orbit from the center of the earth is given as
Pg = -GM/R
Where G is the gravitational constant 6.67x10^-11 N-m^2kg^-2
M is the mass of the earth = 5.98x10^24 kg
R is the distance from that point to the center of the earth = r + Re
r is the distance above earth surface, Re is the earth's radius.
R = 1610 km + 6370 km = 7980 km
Pg = -(6.67x10^-11 x 5.98x10^24)/7980x10^3
Pg = -49983208.02 J/kg
The negative sign means that the gravitational potential is higher away from earth than it is at the earth's surface (it shows convention).
This indicates the kinetic energy per kilogram that the chest of jewel will fall with to earth.
Gravitation Potential on earth's surface is
Pg = -GM/Re
= -(6.67x10^-11 x 5.98x10^24)/6370x10^3 = -62616326.53 J/kg
Difference in gravity potential = -49983208.02 - (-62616326.53)
= 12633118.51 J/kg
The velocity V of the jewel chest will be
0.5v^2 = 12633118.51
V^2 = 25266237.02
V = 5026.55 m/s
Technically, carrying her team-mate horizontally
along a level surface (D) doesn't require any 'work'.
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