The magnitude of the gravitational force between a satellite of mass kg and Earth of…

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The magnitude of the gravitational force between a satellite of mass

m = 5.0\times 10^{2}\,

kg and Earth of mass

M = 5.97\times 10^{24}\,

kg is given by

F = \dfrac{G M m}{r^{2}}

, where

G = 6.67\times 10^{-11}\,

N·m

^{2}

·kg

^{-2}

and

r

is the distance between their centers. When

r = 7.0\times 10^{6}\,

m, the satellite is moving toward Earth so that

dr/dt = -15\,

m·s

^{-1}

. Which of the following is the best estimate of

dF/dt

at that instant? (a)

3.5\times 10^{-5}\,

N·s

^{-1}

(b)

8.7\times 10^{-3}\,

N·s

^{-1}

(c)

\phantom{-}1.7\times 10^{-2}\,

N·s

^{-1}

(d)

-1.7\times 10^{-2}\,

N·s

^{-1}