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Akhilesh Gandhi Grade: 11
        

a shell vertically fired from earth with velocity v/n where v is escape velocity and n is some no. greater than 1neglecting the air resistance calculate the max. altitude attained by shell???

6 years ago

Answers : (2)

SAGAR SINGH - IIT DELHI
879 Points
										

Dear student,


Take this hint:


Apply Pythagoras’ theorem to the right-angled triangle to establish that the appropriate speed for a circular orbit just above the earth’s atmosphere is given by   


 


(Use the approximation that the distance traveled in one second is tiny compared to the radius of the earth.)


























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6 years ago
vikas askiitian expert
510 Points
										

in case of conservative forces we can apply conservation of energy ,so


initial total energy (TE)= PE + KE


PE = -GMm/R      (at surface)


KE=mv2/2n2      


v = (2GM/R)1/2   (escape speed)         so


KE = GMm/n2R


so total energy = KE + PE = GMm/n2R - GMm/R                  ..................1


finally  particle reaches to max height (x distance from surface)& its velocity becomes 0 ...


TE = PE + KE


PE = -GMm/(R+x) 


KE = 0


TE = -GMm/(R+x)           ....................2


since energy is conserved so eq 1 = eq 2


-GMm/(R+x) = -GMm/R + GMm/n2R


 X = R/(n2-1)                   (max altitude)


approve my ans if u like it

6 years ago
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