Question

Help me with this high school physics question!

Answer 1

`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\\\\`