Question

Newton's Law of Gravitation can be used to show that if an object weighs w pounds on the surface of the earth, then its weight at distance x from the center of the earth is W(x) = wR2 x2 (for x ≥ R) where R = 3,960 miles is the radius of the earth. Estimate the weight change, at altitude h, per mile of altitude gained for a 120-lb pilot.

Answer 1

Answer:

W'(x) = $\frac{-240R^2}{h^3}$

Here, the negative sign depicts the loss in weight

Step-by-step explanation:

Data provided in the question :

Function:

W(x) = $\frac{wR^2}{x^2}$

Here,

R = 3,960 miles is the radius of the earth

w = Weight of the pilot = 120 lb

x is the distance from the center of the earth

Therefore,

Rate of change of weight

W'(x) = $\frac{d(\frac{wR^2}{x^2})}{dx}$

or

W'(x) = $\frac{(-2)wR^2}{x^3}$

on substituting the respective values, we get

W'(x) = $\frac{(-2)(120)R^2}{(h)^3}$

or

W'(x) = $\frac{-240R^2}{h^3}$

Here, the negative sign depicts the loss in weight