Question

Not sure where to begin with this problem. Can someone help please? The question is attached as an image.

Answer 1

what grade level is this stuff?

Answer 2

calculus in college

Answer 3

:O

Answer 4

LOL

Answer 5

i'm not sure what they want here but we can say that if the corresponding increase in g is y, then
g + y = GM/(r+x)^2
y = GM/(r+x)^2 - g
= GM/(r+x)^2 - GM/r^2

Answer 6

you start with function
\[ g(r) = G M r^{-2} \]
and find the derivative with respect to r
\[ \frac{dg}{dr} = -2 GM r^{-3} = -2 \frac{GM}{r^2} \cdot \frac{1}{r} \]
The infinitesimals are exact, and the approximation is
\[ \frac{\Delta g}{\Delta r} \approx -2 \frac{GM}{r^2} \cdot \frac{1}{r} \]

solve for \( \Delta g\):
\[ \Delta g\approx -2 \frac{GM}{r^2} \cdot \frac{\Delta r}{r} \]
now replace \( \Delta r\) with x (per the question)
and notice you can replace GM/r^2 with g

Answer 7

okay so the first part of the question is -2x/r

Answer 8

do you know how to do the third part?

Answer 9

@jim_thompson5910 hey do you know how to do the third part of this question?

Answer 10

for the third part you need to calculate \(\Large \Delta g\) for the mountain (to the sea level) and then divide that result by the initial g when at sea level

Answer 11

i'm not sure what delta g is supposed to be

Answer 12

@jim_thompson5910

Answer 13

it's the change in acceleration of gravity

Answer 14

\(\Large \Delta g = \) (value of g at peak of mountain) - (value of g at sea level)

Answer 15

is the value of the mountain 14,000?

Answer 16

no, you need to add the height of the mountain to the radius of the earth

then use the formula given