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.

W'(x) =

Here, the negative sign depicts the loss in weight

Step-by-step explanation:

Data provided in the question :

Function:

W(x) =

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) =

or

W'(x) =

on substituting the respective values, we get

W'(x) =

or

W'(x) =

Here, the negative sign depicts the loss in weight