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Help me with this high school physics question!

Help me with this high school physics question!-example-1
User Tameca
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1 Answer

29 votes
29 votes

Answer:


6.373219 * 10^6 \; meters
or

\rm 6.373 * 10^6 \; meters\; or\;3 \;significant \;decimal \;digits

Step-by-step explanation:

The gravitational force can be calculated with the formula:

\boxed {F_g=(GMm)/(R^2)}

where

\rm F_g = gravitational \; force\\G = gravitational constant\\M = mass\;of\;earth\\m = mass\; of\; the \; person\\

\rm R\;=\;distance\;from\;center\;of\;earth\;to\;surface

Multiplying both sides of the above equation by R and dividing both sides by
\rm F_g gives us a R² in terms of the others

==>
\rm R^2 = (GMm)/(F_g) (1)

Given


F_g = 1030 N, M = 5.97* 10^24\;kg\; \;and \;m = 105kg\\\\

and knowing that
\rm G = 6.67 * 10^(-11) \; Nm^2/kg^2

substitute these values to get


\rm R^2 =((6.67 * 10^(-11))(5.97 * 10^(24))(105))/(1030)


\rm 4.05931 * 10^(13) = 40.5931 * 10^(10)\\\\R = \sqrt{40.5931 x 10^(12)} \\\\= 6.373219 * 10^6 \; meters\\\\

User Sabbour
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