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Question

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


A

h=R(2gRv21)

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B

h=R(2gRv2+1)

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C

h=R(2gRv21)

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D

h=R(2gRv2+1)

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Solution

The correct option is A

h=R(2gRv21)


On the surface of the earth, the total energy is
KEi+PEi=12mv2GmMR
where m is the mass of the rocket and M that of the earth. At the highest point, v = 0 and the energy is entirely potential.
PEf=GmM(R+h) where h is the maximum height attained.
From the law of conservation of energy, we have
12mv2GmMR=GmM(R+h)
R+hh=2gRv2(g=GMR2)
h=R(2gRv21)
Hence, the correct choice is (a).


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