A rocket is launched vertically from the surface of the earth of radius fi with an initial speed v. If atmospheric resistance is neglected, the maximum height h attained by the rocket is given by

Question

Infinity Learn · Accepted Answer

The total energy on the surface of the earth is given $$byT=$$ K.E. $$+$$ P.E. $$=12mv2$$−(GmM/R)where$$ m is the mass of rocket. At highest point, y $$=0$$. Thus at a distance $${R+h) i.e .highest point, the energy is entirely potential. So, energy at highest point is given by P.E. $$=$$−[$$GMm/(R+h)$$]According to law of conservation of $$energy12mv2$$−$$GmMR=$$−$$GMm(R+h)or$$ $$12mv2=GmM1R$$−$$1R+hor$$ $$v22=GMhR(R+h)or$$ $$R+hR=2gRv2$$ ∵$$g=GMR2h=R2gRv2$$−$$1$$

A rocket is launched vertically from the surface of the earth of radius fi with an initial speed v. If atmospheric resistance is neglected, the maximum height h attained by the rocket is given by

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