Show that the variation of gravity with height can be accounted for approximately by the following potential energy function: mgz(1-²) in which r, is the radius of the Earth. Find the force given by the above potential function. From this find the component differential equations of motion of a projectile under such a force. If the vertical component of the initial velocity is to how high does the projectile go? V=mgz
Show that the variation of gravity with height can be accounted for approximately by the following potential energy function: mgz(1-²) in which r, is the radius of the Earth. Find the force given by the above potential function. From this find the component differential equations of motion of a projectile under such a force. If the vertical component of the initial velocity is to how high does the projectile go? V=mgz
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Transcribed Image Text:Show that the variation of gravity with height can be accounted for approximately by the
following potential energy function:
V=mp (1-4)
in which re is the radius of the Earth. Find the force given by the above potential function.
From this find the component differential equations of motion of a projectile under such
a force. If the vertical component of the initial velocity is voz, how high does the projectile
go?
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