A Rocket ship launched from the north pole runs out of fuel, when it is 6370 km

Question

A Rocket ship launched from the north pole runs out of fuel, when it is 6370 km above the earth's surface, at which point is travelling at 4000 m/s. a) How much further does it travel before coming to rest? b) What speed would be required at the new height to escape the earth's gravity altogether? c) Now going back to the conditions of part a), calculate the speed, with which it hits the ground, when it eventually falls back to Earth. d) Going back again to part a, and assuming that you could use the mgh formula to do the same calculation, what would be the average value of "g" you would have to use?

Explanation / Answer

Q.1 a) using kinematic equation: u^2 = 2gh

h ( height reached) = u^2/2g = 4000^2 / ( 19.6) = 816326.53 m or 816.326 km apprx

b) Ve ( escape velocity ) = sqroot ( GM/ r+h) = sqroot ( 6.67 x 10^-11x 5.97 x 10^ 24/ ( 6371 x 10^3 + 7186.326 x 10^3)= sqroot ( 39.82 x 10^ 10 / 13557.326 ) = 5419.554 m/s

c) u^ 2= 2gh

u = sqroot ( 2gh) = sqroot ( 2x 9.8 x 7186.326 x 10^3)= 11868.1 m/s

d)1/2 mv^2 = mgh

0.5 v^2 = gh

0.5 (4000) ^2 = g (816326.53)

g = 9.8 m/s ^2

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