It is a fundamental law of Physics that the force the Earth exerts on an object 5) varies inversely as the square of its' distance from the Earth's center. Thus, an object's weight F(x) is related to its' distance x from the Earth's center by a formula of the form k F(x) =. k is a constant of proportionality whose value depends on the mass of the object and the units of force and distance. Of course, to move an object AWAY from Earth, the Force required is at least its' weight at a given distance x...hence F(x) can also be used as a Force function. SpaceX's retired Dragon spacecraft, which was used to help supply the International Space Station (ISS), weighs approximately 4.65 tons "dry" (unloaded) on the surface of the Earth. a) Assuming that the Earth is a sphere of radius 4000 miles, solve the equation k 4.65 = to discover the constant k in the Force formula mentioned 4000? above. Then, write F(x) out with that specific k value installed. This will be the Force model that pertains to the Dragon specifically.

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Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
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ONLY ANSWER 5A, POSTING SEPERATE QUESTION FOR 5B AND 5C

It is a fundamental law of Physics that the force the Earth exerts on an object
varies inversely as the square of its' distance from the Earth's center. Thus, an object's
weight F(x) is related to its' distance x from the Earth's center by a formula of the form
k
F(x) =
x?
k is a constant of proportionality whose value depends on the mass of the object and
the units of force and distance. Of course, to move an object AWAY from Earth, the
Force required is at least its' weight at a given distance x..hence F(x) can also be used
5)
as a Force function.
SpaceX's retired Dragon spacecraft, which was used to help supply the International
Space Station (ISS), weighs approximately 4.65 tons "dry" (unloaded) on the surface of
the Earth.
a)
Assuming that the Earth is a sphere of radius 4000 miles, solve the equation
k
5 to discover the constant k in the Force formula mentioned
4.65 =
4000
above. Then, write F(x) out with that specifick value installed.
This will be the Force model that pertains to the Dragon specifically.
Evaluate the force model from part a to find the amount of force necessary to
b)
move the Dragon a small distance away from Earth when it is already located at
an altitude of 150 miles above Earth's surface (x = 4150 miles).
c)
Use integration to find the amount of Work necessary to move the Dragon from
the Earth's surface to the orbital altitude of the ISS, which is about 250 miles
above Earth's surface.
Transcribed Image Text:It is a fundamental law of Physics that the force the Earth exerts on an object varies inversely as the square of its' distance from the Earth's center. Thus, an object's weight F(x) is related to its' distance x from the Earth's center by a formula of the form k F(x) = x? k is a constant of proportionality whose value depends on the mass of the object and the units of force and distance. Of course, to move an object AWAY from Earth, the Force required is at least its' weight at a given distance x..hence F(x) can also be used 5) as a Force function. SpaceX's retired Dragon spacecraft, which was used to help supply the International Space Station (ISS), weighs approximately 4.65 tons "dry" (unloaded) on the surface of the Earth. a) Assuming that the Earth is a sphere of radius 4000 miles, solve the equation k 5 to discover the constant k in the Force formula mentioned 4.65 = 4000 above. Then, write F(x) out with that specifick value installed. This will be the Force model that pertains to the Dragon specifically. Evaluate the force model from part a to find the amount of force necessary to b) move the Dragon a small distance away from Earth when it is already located at an altitude of 150 miles above Earth's surface (x = 4150 miles). c) Use integration to find the amount of Work necessary to move the Dragon from the Earth's surface to the orbital altitude of the ISS, which is about 250 miles above Earth's surface.
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