An astronaut r thousand miles from the center of the earth w

An astronaut r thousand miles from the center of the earth weighs 2850/r^2 pounds. The surface of the earth is 4000 miles from the center. (a) If the astronaut is h miles above the surface of the earth, express r as a function of h. Enter your answer as an equation, such as r = 5h - 1. (b) Express the astronaut\'s weight w, in pounds, as a function of h. Enter your answer as an equation, such as w = 5h - 1.

Solution

(a). The surface of the earth is 4000 miles from its center, so that when the astronaut is h miles above the surface of the earth , his distance from the center of earth is 4000 + h miles = (4+h/1000)*1000 miles.   If his distance from the center of the earth is also r thousand miles, then r = 4+h/1000 = 4 +0.001h.

(b) When the astronaut is r thousand miles from the cener of the earth, his weight is 2850/r² pounds. Here, r = 4 +0.001h.Therefore, the astronaut’s weight is w = 2850/(4+0.001h)² pounds.