Calculus Question

Question

The gravitational force, F , on a rocket at a distance, r , from the center of the earth is given by

F= k/r²

where K= 10¹³ newtons * km² . When the rocket is 10⁴ km from the center of the earth it is moving away at  0.3 km/sec. How fast is the gravitational force changing at that moment?

Answer 1

F=k/r² dF/dt = - 2k/r³ dr/dt where dr/dt = .3km/sec r= 10⁴ km and k=10¹³new-km² solving for dF/dt

gives -2x10¹³ n-km²/ 10¹² km³( .3km/sec) hence dF/dt = - 6 new/sec.