Question 127600
{{{W=Cr^(-2)}}} Start with the given equation



{{{W=C(1/r^2)}}} Rewrite {{{r^(-2)}}} as {{{1/r^2}}}



{{{W=C/r^2}}} Multiply



So we're going to use the equation {{{W=C/r^2}}} for parts i) and ii)



i)


In order to do this problem, we need to convert 282 feet into miles. To do this, simply multiply 282 feet by {{{1_mile/5820_feet}}} like this:



{{{(282cross(feet)/1)*(1_mile/5820cross(feet))=(282/5280)miles=0.05341miles}}}


So 282 feet is equivalently 0.05341 miles.


Now simply subtract 0.05341 miles from 3963 miles. We're subtracting because the distance should shrink (ie we're getting closer to the center, so the distance should be smaller)


{{{3963-0.05341=3962.94659}}}



So the distance from the center of the earth to death valley is about 3,962.94659 miles




{{{W=C/r^2}}} Start with the given equation



{{{W=1570536900/0.05341^2}}} Plug in {{{C=1570536900}}} and {{{r=3962.94659}}}



{{{W=1570536900/15704945.6751927}}} Square 3962.94659 to get 15,704,945.6751927



{{{W=100.002695487243}}} Divide



So the object now weighs 100.002695 pounds





ii)


First convert 20,430 feet to miles


{{{(20430cross(feet)/1)*(1_mile/5820cross(feet))=(20430/5280)miles=3.86932miles}}}



So 20,430 feet is 3.86932 miles



Now add 3.86932 miles to 3963 miles. We're add because the distance should get larger (ie now we're moving away from the center, so the distance should increase)


{{{3963+3.86932=3966.86932}}}



So the distance from the center to the peak is about 3,966.86932 miles




{{{W=C/r^2}}} Start with the given equation



{{{W=1570536900/3966.86932^2}}} Plug in {{{C=1570536900}}} and {{{r=3966.86932}}}



{{{W=1570536900/15736052.2019572}}} Square 3,966.86932 to get 15,736,052.2019572



{{{W=99.8050133441131}}} Divide



So the object now weighs 99.805013 pounds