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Question

A rocket is launched vertically from the surface of earth with an initial velocity v. How far above the surface of earth it will go? Neglect the air resistance.

A
R(2gRv21)1/2
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B
R(2gRv21)
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C
R(2gRv21)1
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D
R(2gRv21)2
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Solution

The correct option is D R(2gRv21)1
By conservation of energy,
Kinetic energy of launched rocket = change in potential energy of rocket at maximum height.
Ig h is maximum height reached:
12mv2=mgh(RR+h)R+hh=2gRv2h=R(2gRv21)1

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